This table gives the list of problem which are kovacic type. These are second order
linear ODE’s with rational coefficients which can be solved using Kovacic’s
algorithm. I have not yet implemented this algorithm. These are detected by calling
DEtools:-kovacicsols(ode,y(x)) and if no error is generated and if solution is
found, then the order is flagged in the database as kovacic by setting the field
is_kovacic=1
Number of problems in this table is 5471
|
Table 2.658: Summary of results
|
|||
|
# |
ODE |
Solved? |
Verified? |
|
|
|||
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-15 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+3 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+8 y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 y^{\prime \prime }-7 y^{\prime }-20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}35 y^{\prime \prime }-y^{\prime }-12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 3 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 12 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 6 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y = 4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y = 6 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y = 6 x +4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-3 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-7 y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 y^{\prime \prime }+6 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 i y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-i y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \left (-2+2 i \sqrt {3}\right ) y \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\frac {x^{\prime \prime }}{2}+3 x^{\prime }+4 x = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{\prime \prime }+30 x^{\prime }+63 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+8 x^{\prime }+16 x = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{\prime \prime }+12 x^{\prime }+50 x = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{\prime \prime }+20 x^{\prime }+169 x = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{\prime \prime }+16 x^{\prime }+40 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+10 x^{\prime }+125 x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 3 x +4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 2 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 3 x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+4 y^{\prime }+7 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = \sinh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = \cosh \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 1+x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 2 \cos \left (3 x \right )+3 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 2 x^{2} {\mathrm e}^{3 x}+5 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 3 x \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = x \left (-{\mathrm e}^{-2 x}+{\mathrm e}^{-x}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = x \,{\mathrm e}^{3 x} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 1+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sin \left (x \right )^{4} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x \cos \left (x \right )^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 4 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 3 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = \sinh \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \cos \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 2 \sec \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \csc \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{4} \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 8 x^{\frac {4}{3}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}-1 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+9 x = 10 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x = 5 \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+100 x = 225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+25 x = 90 \cos \left (4 t \right ) \] |
✓ |
✓ |
|
|
\[ {}m x^{\prime \prime }+k x = F_{0} \cos \left (\omega t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 10 \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+3 x^{\prime }+5 x = -4 \cos \left (5 t \right ) \] |
✓ |
✓ |
|
|
\[ {}2 x^{\prime \prime }+2 x^{\prime }+x = 3 \sin \left (10 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+3 x^{\prime }+3 x = 8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+5 x = 10 \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+2 x^{\prime }+26 x = 600 \cos \left (10 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+8 x^{\prime }+25 x = 200 \cos \left (t \right )+520 \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-\left (2+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+16 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-16 y^{\prime \prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime }-3 y^{\prime \prime }-2 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime \prime }+2 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+10 y^{\prime \prime }+25 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime }-y^{\prime \prime }-5 y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+100 y^{\prime }-500 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime } = y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+2 y \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 4 y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (-1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (-1+x \right ) y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (4 x^{2}+16 x +17\right ) y^{\prime \prime } = 8 y \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 y^{\prime \prime }-y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-3 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 y^{\prime \prime }-5 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-3 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\left (2 \alpha -1\right ) y^{\prime }+\alpha \left (\alpha -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (3-\alpha \right ) y^{\prime }-2 \left (\alpha -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+3 y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}y^{\prime \prime }+2 y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}9 y^{\prime \prime }+9 y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }-u^{\prime }+2 u = 0 \] |
✓ |
✓ |
|
|
\[ {}5 u^{\prime \prime }+2 u^{\prime }+7 u = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 a y^{\prime }+\left (a^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+4 t y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+\frac {5 y}{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 y^{\prime \prime }+6 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-4 y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+12 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+17 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}16 y^{\prime \prime }+24 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}25 y^{\prime \prime }-20 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 y^{\prime \prime }+6 y^{\prime }+82 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+12 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+\frac {y}{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-t \left (2+t \right ) y^{\prime }+\left (2+t \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+2 t y^{\prime }+\frac {y}{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}2 t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 t^{2} y^{\prime \prime }-8 t y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+5 t y^{\prime }+13 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 2 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 16 \,{\mathrm e}^{\frac {t}{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 9 \sec \left (3 t \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 t}}{t^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 3 \csc \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \sec \left (\frac {t}{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = g \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = g \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-t \left (2+t \right ) y^{\prime }+\left (2+t \right ) y = 2 t^{3} \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = t^{2} {\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (-1+t \right )^{2} {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \ln \left (x \right ) x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = g \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 4 t^{2} \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = t^{2} {\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (-1+t \right ) {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+2 u = 0 \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+2 u = 0 \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (\frac {t}{4}\right ) \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (6 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+3\right ) y^{\prime \prime }-3 x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\alpha ^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime \prime }-y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2-t \right ) y^{\prime \prime \prime }+\left (2 t -3\right ) y^{\prime \prime }-t y^{\prime }+y = 0 \] |
✗ |
✗ |
|
|
\[ {}t^{2} \left (3+t \right ) y^{\prime \prime \prime }-3 t \left (2+t \right ) y^{\prime \prime }+6 \left (t +1\right ) y^{\prime }-6 y = 0 \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+4 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (6\right )}-y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+6 y^{\prime \prime }+30 y^{\prime }-36 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\omega ^{2} y = \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t <\infty \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & \pi \le t <2 \pi \\ 0 & \operatorname {otherwise} \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \operatorname {otherwise} \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 1-\operatorname {Heaviside}\left (t -\pi \right ) \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right ) \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2} \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )-\operatorname {Heaviside}\left (t -5-k \right ) \left (t -5-k \right )}{k} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = \sin \left (t \right )+\delta \left (t -3 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 2 \delta \left (t -\frac {\pi }{4}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{2}+y = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{4}+y = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \frac {\operatorname {Heaviside}\left (t -4+k \right )-\operatorname {Heaviside}\left (t -4-k \right )}{2 k} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = f \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-4\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = \left (2 x +1\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = \frac {4}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 7 x^{\frac {3}{2}} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x} \left (1+4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 8 \,{\mathrm e}^{-x \left (2+x \right )} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = -6 x -4 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x \left (-1+x \right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y = x^{3} {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y = x^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}\left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y = \left (4 x^{2}-4 x +1\right ) {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 4 x^{4} \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+\left (1+4 x \right ) y^{\prime }+\left (2 x +1\right ) y = 3 \sqrt {x}\, {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = -{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y = 4 x^{\frac {5}{2}} {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 4 x^{2} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (-2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 4 x^{4} \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y = \left (1+x \right )^{3} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-4\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 2+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \tan \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 x \right ) \sec \left (2 x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {4}{1+{\mathrm e}^{-x}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 3 \,{\mathrm e}^{x} \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 14 x^{\frac {3}{2}} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \frac {4 \,{\mathrm e}^{-x}}{1-{\mathrm e}^{-2 x}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 2 x^{2}+2 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 4 \,{\mathrm e}^{-x \left (2+x \right )} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{\frac {5}{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 2 x^{4} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = \left (2 x +1\right )^{2} {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y = 6 x^{3} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y = x^{1+a} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = x^{3} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{5} \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 8 x^{\frac {5}{2}} \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y = x^{\frac {7}{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y = 3 x^{4} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = x^{3} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = x^{\frac {3}{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+2 \left (x +3\right ) y = x^{4} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (2+x \right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 2 x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = x^{4} \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 2 \left (-1+x \right )^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y = x^{\frac {5}{2}} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = \left (3 x -1\right )^{2} {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }+2 y = \left (-1+x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 x \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = -2 x^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right ) \left (2 x +3\right ) y^{\prime \prime }+2 \left (2+x \right ) y^{\prime }-2 y = \left (2 x +3\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (6 x +4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+3 x \right ) y^{\prime \prime }+x \left (x^{2}+12 x +2\right ) y^{\prime }+2 x \left (x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }-9 x y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\left (x -3\right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}-4 x +1\right ) y^{\prime \prime }+10 \left (-1+x \right ) y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (-2+x \right ) y^{\prime }+36 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (3 x^{2}+6 x +5\right ) y^{\prime \prime }+9 \left (1+x \right ) y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-4\right ) y^{\prime \prime }-x y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (1+x \right ) y^{\prime }+60 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-2 x^{3}+1\right ) y^{\prime \prime }-10 x^{2} y^{\prime }-8 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-2 x^{3}+1\right ) y^{\prime \prime }+6 x^{2} y^{\prime }+24 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{6}+1\right ) y^{\prime \prime }-12 x^{5} y^{\prime }-30 x^{4} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+3 x \right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+8 x \right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-2 x^{2}+1\right ) y^{\prime \prime }+\left (2-6 x \right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+3 x +3\right ) y^{\prime \prime }+\left (6+4 x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x +4\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}-3 x +2\right ) y^{\prime \prime }-\left (4-6 x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (1+x \right ) y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-x +1\right ) y^{\prime \prime }-\left (1-4 x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (4 x +2\right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+3 x +1\right ) y^{\prime \prime }+\left (6+8 x \right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (6 x^{2}-5 x +1\right ) y^{\prime \prime }-\left (10-24 x \right ) y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (4 x^{2}-4 x +1\right ) y^{\prime \prime }-\left (8-16 x \right ) y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+4 x +4\right ) y^{\prime \prime }+\left (8+4 x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (3 x^{2}+8 x +4\right ) y^{\prime \prime }+\left (16+12 x \right ) y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (1+x \right ) y^{\prime }-\left (1-4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}12 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}18 x^{2} \left (1+x \right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (5+4 x \right ) y^{\prime }-\left (1-2 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x \left (5+x \right ) y^{\prime }-\left (2-3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-2 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-\left (1+3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (5+18 x \right ) y^{\prime }-\left (1-12 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2+x \right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+8\right ) y^{\prime \prime }+7 x \left (x^{2}+2\right ) y^{\prime }-\left (-9 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} \left (1+x \right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (7 x^{2}+6 x +3\right ) y^{\prime }+\left (-3 x^{2}+6 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+2 x +1\right ) y^{\prime \prime }+x \left (4 x^{2}+3 x +1\right ) y^{\prime }-x \left (1-2 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (1+x \right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} \left (1+x \right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (-x +3\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-4 x \right ) y^{\prime \prime }+3 x \left (1-6 x \right ) y^{\prime }+\left (1-12 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3+5 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (7 x^{2}+3\right ) y^{\prime }+\left (-3 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }+\left (12 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 x y^{\prime }+\left (1+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (2 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (3+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (4-3 x \right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (2+x \right ) y^{\prime }-\left (2-3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-3 \left (x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }-4 y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y = 0 \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }-x \left (9+8 x \right ) y^{\prime }-12 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (-x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-7 y^{\prime \prime }-y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+7 y^{\prime }-5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+8 y^{\prime \prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+16 y^{\prime }-16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime }+3 y^{\prime \prime }-2 y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+5 y^{\prime \prime }+9 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}27 y^{\prime \prime \prime }+27 y^{\prime \prime }+9 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+12 y^{\prime \prime }+36 y = 0 \] |
✓ |
✓ |
|
|
\[ {}16 y^{\prime \prime \prime \prime }-72 y^{\prime \prime }+81 y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+7 y^{\prime \prime }+5 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+3 y^{\prime \prime }-13 y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime \prime }-y^{\prime \prime }-7 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime }-11 y^{\prime \prime }+12 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}8 y^{\prime \prime \prime }-4 y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+7 y^{\prime \prime }+6 y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-8 y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+19 y^{\prime \prime }+32 y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}+y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = -{\mathrm e}^{x} \left (-24 x^{2}+76 x +4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{-3 x} \left (6 x^{2}-23 x +32\right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y = -{\mathrm e}^{x} \left (6 x^{2}+45 x +4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y = {\mathrm e}^{-2 x} \left (3 x^{2}-17 x +2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y = {\mathrm e}^{x} \left (16 x^{3}+24 x^{2}+2 x -1\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-2 y = {\mathrm e}^{x} \left (15 x^{2}+34 x +14\right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y = -{\mathrm e}^{-2 x} \left (1-15 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = -{\mathrm e}^{x} \left (7+6 x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime }-7 y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{2 x} \left (17+30 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+3 y^{\prime }+9 y = 2 \,{\mathrm e}^{3 x} \left (11-24 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-7 y^{\prime \prime }+8 y^{\prime }+16 y = 2 \,{\mathrm e}^{4 x} \left (13+15 x \right ) \] |
✓ |
✓ |
|
|
\[ {}8 y^{\prime \prime \prime }-12 y^{\prime \prime }+6 y^{\prime }-y = {\mathrm e}^{\frac {x}{2}} \left (1+4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }-7 y^{\prime }+6 y = -3 \,{\mathrm e}^{-x} \left (-8 x^{2}+8 x +12\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-2 y = -3 \,{\mathrm e}^{2 x} \left (11+12 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime } = -16 \,{\mathrm e}^{-2 x} \left (-x^{3}+x^{2}+x +1\right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime \prime }-11 y^{\prime \prime }-9 y^{\prime }-2 y = -{\mathrm e}^{x} \left (1-6 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+2 y = {\mathrm e}^{2 x} \left (x^{4}+x +24\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }-4 y = -{\mathrm e}^{2 x} \left (15 x^{2}+28 x +4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = {\mathrm e}^{x} \left (-3 x^{2}+x +3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{2 x} \left (18 x^{2}+33 x +13\right ) \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-y = {\mathrm e}^{x} \left (11+12 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x} \left (10 x^{2}-24 x +5\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (-5 x^{2}-8 x +3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (\left (16+10 x \right ) \cos \left (x \right )+\left (30-10 x \right ) \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y = {\mathrm e}^{-x} \left (\left (1-22 x \right ) \cos \left (2 x \right )-\left (6 x +1\right ) \sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }-2 y = {\mathrm e}^{2 x} \left (\left (-x^{2}+5 x +27\right ) \cos \left (x \right )+\left (9 x^{2}+13 x +2\right ) \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y = -{\mathrm e}^{x} \left (\left (4 x^{2}+5 x +9\right ) \cos \left (2 x \right )-\left (-3 x^{2}-5 x +6\right ) \sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }+12 y = 8 \cos \left (2 x \right )-16 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+2 y = {\mathrm e}^{x} \left (\left (20+4 x \right ) \cos \left (x \right )-\left (12+12 x \right ) \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-7 y^{\prime \prime }+20 y^{\prime }-24 y = -{\mathrm e}^{2 x} \left (\left (13-8 x \right ) \cos \left (2 x \right )-\left (-4 x +8\right ) \sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+18 y^{\prime } = -{\mathrm e}^{3 x} \left (\left (2-3 x \right ) \cos \left (3 x \right )-\left (3+3 x \right ) \sin \left (3 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-8 y^{\prime }-8 y = {\mathrm e}^{x} \left (8 \cos \left (x \right )+16 \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }-4 y = {\mathrm e}^{x} \left (2 \cos \left (2 x \right )-\sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+15 y = {\mathrm e}^{2 x} \left (15 x \cos \left (2 x \right )+32 \sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+13 y^{\prime \prime }+12 y^{\prime }+4 y = {\mathrm e}^{-x} \left (\left (4-x \right ) \cos \left (x \right )-\left (5+x \right ) \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }-4 y = -{\mathrm e}^{-x} \left (-\sin \left (x \right )+\cos \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y = {\mathrm e}^{x} \left (\sin \left (2 x \right )+\cos \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+32 y^{\prime \prime }+64 y^{\prime }+39 y = {\mathrm e}^{-2 x} \left (\left (4-15 x \right ) \cos \left (3 x \right )-\left (4+15 x \right ) \sin \left (3 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y = {\mathrm e}^{x} \left (\left (7+8 x \right ) \cos \left (2 x \right )+\left (-4 x +8\right ) \sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+8 y^{\prime \prime }+8 y^{\prime }+4 y = -2 \,{\mathrm e}^{x} \left (-\sin \left (x \right )+\cos \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+32 y^{\prime \prime }-64 y^{\prime }+64 y = {\mathrm e}^{2 x} \left (-\sin \left (2 x \right )+\cos \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+26 y^{\prime \prime }-40 y^{\prime }+25 y = {\mathrm e}^{2 x} \left (3 \cos \left (x \right )-\left (1+3 x \right ) \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = {\mathrm e}^{2 x}-4 \,{\mathrm e}^{x}-2 \cos \left (x \right )+4 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 5 \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x}-4 \cos \left (x \right )+4 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+9 y^{\prime }-10 y = 10 \,{\mathrm e}^{2 x}+20 \,{\mathrm e}^{x} \sin \left (2 x \right )-10 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 12 \,{\mathrm e}^{-x}+9 \cos \left (2 x \right )-13 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 4 \,{\mathrm e}^{-x} \left (1-6 x \right )-2 x \cos \left (x \right )+2 \left (1+x \right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = -12 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x}+10 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+11 y^{\prime \prime }-14 y^{\prime }+10 y = -{\mathrm e}^{x} \left (\sin \left (x \right )+2 \cos \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (1+x \right )+{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+9 y^{\prime \prime }+7 y^{\prime }+2 y = {\mathrm e}^{-x} \left (30+24 x \right )-{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y = {\mathrm e}^{x} \left (12 x -2 \cos \left (x \right )+2 \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = {\mathrm e}^{2 x} \left (10+3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-2 y = -{\mathrm e}^{3 x} \left (17 x^{2}+67 x +9\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = {\mathrm e}^{2 x} \left (-3 x^{2}-4 x +5\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = -2 \,{\mathrm e}^{-x} \left (6 x^{2}-18 x +7\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \left (1+x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = -{\mathrm e}^{-x} \left (3 x^{2}-9 x +4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-2 x} \left (\left (23-2 x \right ) \cos \left (x \right )+\left (8-9 x \right ) \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{x} \left (\left (28+6 x \right ) \cos \left (2 x \right )+\left (11-12 x \right ) \sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y = {\mathrm e}^{x} \left (\left (6 x +2\right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{x} \left (1-6 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = -{\mathrm e}^{-x} \left (4-8 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \left (20-12 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y = 30 \cos \left (x \right )-10 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+5 y^{\prime \prime }-2 y^{\prime } = -2 \,{\mathrm e}^{x} \left (-\sin \left (x \right )+\cos \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 2 x \] |
✓ |
✓ |
|
|
\[ {}4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 x y^{\prime }+2 y = 30 x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 x y^{\prime }+9 y = 96 x^{\frac {5}{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 x y^{\prime }+24 y = x^{4} \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = 12 x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 4 x \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 x y^{\prime }-18 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+16 x y^{\prime }-16 y = 9 x^{4} \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = \left (1+x \right ) x \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 9 x^{2} \] |
✓ |
✓ |
|
|
\[ {}4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-x y^{\prime }+y = 6 x \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-6 x y^{\prime }+6 y = 40 x^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = F \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = F \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = F \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = F \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+t y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+t y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 y^{\prime \prime }-7 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }+6 y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+y^{\prime }-10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}5 y^{\prime \prime }+5 y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-t y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+3 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }-2 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 y^{\prime \prime }+6 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+2 t \right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t \,{\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-3 y^{\prime }+y = \left (t^{2}+1\right ) {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = t \,{\mathrm e}^{3 t}+1 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }+4 y^{\prime }+y = \sin \left (t \right ) {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = t^{\frac {5}{2}} {\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \sqrt {t +1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = f \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = t^{2}+1 \] |
✓ |
✓ |
|
|
\[ {}m y^{\prime \prime }+c y^{\prime }+k y = F_{0} \cos \left (\omega t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+t y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (t^{2}+2\right ) y^{\prime \prime }-t y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t \left (2-t \right ) y^{\prime \prime }-6 \left (-1+t \right ) y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-t y^{\prime }+\alpha ^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-5 t y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+t \right )^{2} y^{\prime \prime }-2 \left (-1+t \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (t -2\right )^{2} y^{\prime \prime }+5 \left (t -2\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-\left (t +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-t y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }-\left (4+t \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }+t y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+3 y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+2 y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }-17 y^{\prime }+60 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-9 y^{\prime \prime }+23 y^{\prime }-15 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-7 y^{\prime \prime }-y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-20 y^{\prime \prime }+27 y^{\prime }+18 y = 0 \] |
✓ |
✓ |
|
|
\[ {}12 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+3 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime }+2 y^{\prime \prime }-4 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+24 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-7 y^{\prime \prime }-8 y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+15 y^{\prime \prime }+4 y^{\prime }-12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}+y^{\prime \prime \prime \prime }-13 y^{\prime \prime \prime }-13 y^{\prime \prime }+36 y^{\prime }+36 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-15 y^{\prime \prime \prime }-19 y^{\prime \prime }+30 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\left (5\right )}-3 y^{\prime \prime \prime }-y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-7 y^{\prime \prime }+16 y^{\prime }-12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime }-20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-8 y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+10 y^{\prime }-15 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+11 y^{\prime }-40 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-12 y^{\prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime }+12 y^{\prime \prime }-3 y^{\prime }+14 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }-6 y^{\prime \prime }+8 y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 3 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = x \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = x +{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = {\mathrm e}^{3 x}+\sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}-2 y^{\prime \prime }+3 y = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = x \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime } = x^{2}+8 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{x} \sin \left (3 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-12 y = x +{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y = {\mathrm e}^{4 x} \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = x^{3} {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{2 x} x \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y = \sin \left (k x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 n y^{\prime }+n^{2} y = 5 \cos \left (6 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+9 y = \left (1+\sin \left (3 x \right )\right ) \cos \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 2 x -{\mathrm e}^{-4 x}+\sin \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime } = \left (2 x^{2}+x \right ) {\mathrm e}^{-2 x}+5 \cos \left (3 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y = 8 \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y = 12 \cos \left (x \right )^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = {\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}2 y^{\prime \prime }+y^{\prime } = 8 \sin \left (2 x \right )+{\mathrm e}^{-x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = 3 x \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}2 y^{\prime \prime }+5 y^{\prime }-3 y = \sin \left (x \right )-8 x \] |
✓ |
✓ |
|
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\[ {}8 y^{\prime \prime }-y = x \,{\mathrm e}^{-\frac {x}{2}} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y = x^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = 4 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y = 2 x -2 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y = 3 x +5 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{x}+\sin \left (4 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime } = \cos \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime } = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+a^{2} y = \sec \left (x a \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime } = {\mathrm e}^{2 x}+\sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y = \sec \left (x \right ) \tan \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y = {\mathrm e}^{-x} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+9 y = \sec \left (x \right ) \csc \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+9 y = \csc \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (\frac {x}{3}\right )^{2} \] |
✓ |
✓ |
|
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\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{\frac {x}{2}} \ln \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y = 3 \,{\mathrm e}^{-4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{3 x}}{2}-\frac {{\mathrm e}^{-3 x}}{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-2 y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y = \sin \left (x \right )-{\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 4 \,{\mathrm e}^{x}+3 \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = {\mathrm e}^{3 x} \left (1+\sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 n^{2} y^{\prime }+n^{4} y = \sin \left (k x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y = {\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = x^{2}-8 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime } = {\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime } = {\mathrm e}^{2 x} \left (x -3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime } = \sin \left (3 x \right )+x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = {\mathrm e}^{2 x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }+2 y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = x^{3}-\frac {\cos \left (2 x \right )}{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime } = {\mathrm e}^{-2 x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{-2 x} \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = x \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x^{2} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = x^{2} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+3 y^{\prime }-2 y = x^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime } = x \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = x^{2} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = x^{2} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = x \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = x^{3} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = x \,{\mathrm e}^{2 x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = x \,{\mathrm e}^{2 x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = x^{2} {\mathrm e}^{-x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-16 x y^{\prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }-18 y = \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = \ln \left (x^{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 1-x \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {1}{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 4 x +\sin \left (\ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = \ln \left (x \right ) x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+3 y = \left (-1+x \right ) \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}4 x^{3} y^{\prime \prime \prime }+8 x^{2} y^{\prime \prime }-x y^{\prime }+y = x +\ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 x y^{\prime }+10 y = \frac {4}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 x y^{\prime }-6 y = \cos \left (\ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }-x y^{\prime }+4 y = \sin \left (\ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = k^{2} y \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+k^{2} x = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime } = x^{2}+1 \] |
✓ |
✓ |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime } = y^{\prime } \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (y^{\prime }+1\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+x = y^{\prime } \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+t x^{\prime } = t^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime } = x y^{\prime }+1 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \sec \left (x \right ) \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-k^{2} x = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x +4\right ) y^{\prime \prime }+7 x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+\left (3 x +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (1-x \right ) y^{\prime \prime }+3 x \left (2 x +1\right ) y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (1-3 x \right ) y^{\prime \prime }+5 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }-5 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x +4\right ) y^{\prime \prime }+x \left (-1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}x^{2} y^{\prime \prime }-x \left (1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x^{2}-1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (2 x -1\right ) y^{\prime }+x \left (-1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (3 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (x -4\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-x y^{\prime }+y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}\left (1-2 x \right ) y^{\prime \prime }+4 x y^{\prime }-4 y = x^{2}-x \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+10 x y^{\prime }+y = -1+x \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = x^{3}+1 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 6 \left (-x^{2}+1\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+2 y = x^{2} \left (2+x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (1+x \right ) y = x \left (x^{2}+x +1\right ) \] |
✓ |
✓ |
|
|
\[ {}\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y = x^{2} \left (1+x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\omega _{0}^{2} x = a \cos \left (\omega t \right ) \] |
✓ |
✓ |
|
|
\[ {}f^{\prime \prime }+2 f^{\prime }+5 f = 0 \] |
✓ |
✓ |
|
|
\[ {}f^{\prime \prime }+2 f^{\prime }+5 f = {\mathrm e}^{-t} \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}f^{\prime \prime }+6 f^{\prime }+9 f = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 4 \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }+3 \left (1+x \right ) y^{\prime }+y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (-2+x \right ) y^{\prime \prime }+3 y^{\prime }+\frac {4 y}{x^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = x^{n} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime \prime }+2 y^{\prime \prime } = A x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = {\mathrm e}^{-x^{2}} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y = 0 \] |
✓ |
✓ |
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\[ {}4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
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\[ {}z y^{\prime \prime }-2 y^{\prime }+9 z^{5} y = 0 \] |
✓ |
✓ |
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\[ {}f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f = 0 \] |
✓ |
✓ |
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\[ {}z^{2} y^{\prime \prime }-\frac {3 z y^{\prime }}{2}+\left (z +1\right ) y = 0 \] |
✓ |
✓ |
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\[ {}z y^{\prime \prime }-2 y^{\prime }+y z = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-2 z y^{\prime }-2 y = 0 \] |
✓ |
✓ |
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\[ {}z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z} = 0 \] |
✓ |
✓ |
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\[ {}\left (-z^{2}+1\right ) y^{\prime \prime }-z y^{\prime }+m^{2} y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-25 y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-9 y = 0 \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \] |
✓ |
✓ |
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\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 9 x^{2} \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \left (x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-\left (a +b \right ) y^{\prime }+y a b = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime } = x^{n} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime } = \cos \left (x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-8 y = 0 \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \ln \left (x \right ) x^{2} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x} = 9 x \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-36 y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+4 y^{\prime } = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-18 y^{\prime }-40 y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime } = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime } = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+36 y = 0 \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = 0 \] |
✓ |
✓ |
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\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \] |
✓ |
✓ |
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\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
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\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 x y^{\prime } = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+y^{\prime }-6 y = 18 \,{\mathrm e}^{5 x} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+y^{\prime }-2 y = 4 x^{2}+5 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = 4 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y = 24 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime } = 6 \,{\mathrm e}^{-x} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+y = 6 \,{\mathrm e}^{x} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 5 \,{\mathrm e}^{-2 x} x \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+4 y = 8 \sin \left (2 x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y = 4 x^{2} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 9 \,{\mathrm e}^{-x} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 2 \,{\mathrm e}^{-x}+3 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+9 y = 5 \cos \left (2 x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-y = 9 \,{\mathrm e}^{2 x} x \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+y^{\prime }-2 y = -10 \sin \left (x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+y^{\prime }-2 y = 4 \cos \left (x \right )-2 \sin \left (x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+\omega ^{2} y = \frac {F_{0} \cos \left (\omega t \right )}{m} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-4 y^{\prime }+6 y = 7 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = 4 x \,{\mathrm e}^{x} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime \prime }+104 y^{\prime \prime \prime }+2740 y^{\prime \prime } = 5 \,{\mathrm e}^{-2 x} \cos \left (3 x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+6 y = \sin \left (x \right )^{2} \cos \left (x \right )^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-16 y = 20 \cos \left (4 x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+2 y^{\prime }+y = 50 \sin \left (3 x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-y = 10 \,{\mathrm e}^{2 x} \cos \left (x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 169 \sin \left (3 x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-y^{\prime }-2 y = 40 \sin \left (x \right )^{2} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+y = 3 \,{\mathrm e}^{x} \cos \left (2 x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 2 \,{\mathrm e}^{-x} \sin \left (x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-4 y = 100 x \,{\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x} \cos \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+10 y = 24 \,{\mathrm e}^{x} \cos \left (3 x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+16 y = 34 \,{\mathrm e}^{x}+16 \cos \left (4 x \right )-8 \sin \left (4 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 4 \,{\mathrm e}^{3 x} \ln \left (x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+9 y = 18 \sec \left (3 x \right )^{3} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-4 y = \frac {8}{{\mathrm e}^{2 x}+1} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \tan \left (x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+9 y = \frac {36}{4-\cos \left (3 x \right )^{2}} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = \frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 4 \,{\mathrm e}^{3 x} \sec \left (2 x \right )^{2} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+y = \sec \left (x \right )+4 \,{\mathrm e}^{x} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+y = \csc \left (x \right )+2 x^{2}+5 x +1 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-y = 2 \tanh \left (x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-2 m y^{\prime }+m^{2} y = \frac {{\mathrm e}^{m x}}{x^{2}+1} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {4 \,{\mathrm e}^{x} \ln \left (x \right )}{x^{3}} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+2 y^{\prime }+y = \frac {{\mathrm e}^{-x}}{\sqrt {-x^{2}+4}} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+2 y^{\prime }+17 y = \frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {4 \,{\mathrm e}^{-2 x}}{x^{2}+1}+2 x^{2}-1 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 15 \,{\mathrm e}^{-2 x} \ln \left (x \right )+25 \cos \left (x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = \frac {2 \,{\mathrm e}^{x}}{x^{2}} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 36 \,{\mathrm e}^{2 x} \ln \left (x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = \frac {2 \,{\mathrm e}^{-x}}{x^{2}+1} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime } = 12 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-9 y = F \left (x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = F \left (x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+y^{\prime }-2 y = F \left (x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = F \left (x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 5 \,{\mathrm e}^{2 x} x \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right ) \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \cos \left (x \right ) \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 9 \ln \left (x \right ) \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 8 x \ln \left (x \right )^{2} \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \left (x \right ) \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+6 y = 4 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \frac {x^{2}}{\ln \left (x \right )} \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y = x^{m} \ln \left (x \right )^{k} \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 0 \] |
✓ |
✓ |
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\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+25 y = 0 \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
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\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
✓ |
✓ |
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\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
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\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}+4 x^{2} y = 0 \] |
✓ |
✓ |
|
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\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+y = \csc \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x} x^{2} \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 8 x^{4} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 15 \,{\mathrm e}^{3 x} \sqrt {x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 4 \,{\mathrm e}^{2 x} \ln \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}4 x^{2} y^{\prime \prime }+y = \sqrt {x}\, \ln \left (x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime \prime }+11 y^{\prime \prime }+36 y^{\prime }+26 y = 0 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 4 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 4 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime } = x^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime } = \sin \left (4 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y = 8 \,{\mathrm e}^{-x}+1 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-4 y = 5 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 x \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y = 4 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y = \ln \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 5 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = 4 \cos \left (2 x \right )+3 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-12 y = 36 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y^{\prime }-2 y = 10 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 \,{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime } = 30 \,{\mathrm e}^{-3 t} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y = 12 \,{\mathrm e}^{2 t} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y = 10 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-6 y = -6 \,{\mathrm e}^{t}+12 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y = 6 \cos \left (t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-9 y = 13 \sin \left (2 t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y = 8 \sin \left (t \right )-6 \cos \left (t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-2 y = 10 \cos \left (t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 3 \cos \left (t \right )+\sin \left (t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y = 9 \sin \left (t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = 6 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+9 y = 7 \sin \left (4 t \right )+14 \cos \left (4 t \right ) \] |
✓ |
✓ |
|
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|||
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\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y = \operatorname {Heaviside}\left (-1+t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-2 y = 1-3 \operatorname {Heaviside}\left (t -2\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-4 y = \operatorname {Heaviside}\left (-1+t \right )-\operatorname {Heaviside}\left (t -2\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = t -\operatorname {Heaviside}\left (-1+t \right ) \left (-1+t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = -10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y^{\prime }-6 y = 30 \operatorname {Heaviside}\left (-1+t \right ) {\mathrm e}^{1-t} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 5 \operatorname {Heaviside}\left (t -3\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-4 y = \delta \left (t -3\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -\frac {\pi }{2}\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = \delta \left (t -2\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+9 y = 15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+16 y = 4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-x^{2} y^{\prime }-2 x y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \] |
✓ |
✓ |
|
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\[ {}\left (x^{2}-3\right ) y^{\prime \prime }-3 x y^{\prime }-5 y = 0 \] |
✓ |
✓ |
|
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\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
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\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0 \] |
✓ |
✓ |
|
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\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+x y^{\prime }+\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }-4 y = 6 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}4 x y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }-x \left (x +8\right ) y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }+x \left (7+3 x \right ) y^{\prime }+\left (6 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x \left (2+x \right ) y^{\prime }+2 \left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-6 x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (4 x^{2}+1\right ) y^{\prime \prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\frac {3 x y^{\prime }}{2}-\frac {\left (1+x \right ) y}{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }+9 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+5 y^{\prime \prime }+5 y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+10 y = 3 x \,{\mathrm e}^{-3 x}-2 \,{\mathrm e}^{3 x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = \left (x +{\mathrm e}^{x}\right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sinh \left (x \right ) \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \cosh \left (x \right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y = {\mathrm e}^{2 x} \sin \left (2 x \right )+2 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+3 y^{\prime } = x^{2}+{\mathrm e}^{2 x} x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime } = 7 x -3 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = \sin \left (x \right ) \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 y^{\prime \prime }-11 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 k y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-11 y^{\prime \prime }-12 y^{\prime }+36 y = 0 \] |
✓ |
✓ |
|
|
\[ {}36 y^{\prime \prime \prime \prime }-37 y^{\prime \prime }+4 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+36 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{i x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 2 \,{\mathrm e}^{2 x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x^{2}+2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x +\sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 4 x \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = x \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-2 x}+x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = x +{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right )+{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (2 x \right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 8 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{x} \left (2 x -3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cot \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 4 x \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \csc \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = \frac {{\mathrm e}^{-x}}{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{-x}\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = x \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = {\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = x^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (y^{\prime }+1\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0 \] |
✓ |
✓ |
|
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\[ {}x^{4} y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✗ |
✗ |
|
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\[ {}x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
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\[ {}\left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
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\[ {}\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0 \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (\left (-n +1\right ) x -\left (6-4 n \right ) x^{2}\right ) y^{\prime }+n \left (-n +1\right ) x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y = 0 \] |
✓ |
✓ |
|
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\[ {}\left (a^{2}+x^{2}\right ) y^{\prime \prime }+x y^{\prime }-n^{2} y = 0 \] |
✓ |
✓ |
|
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\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+a^{2} y = 0 \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }+\left (3 x -1\right ) y = 0 \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
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\[ {}2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = \sqrt {x} \] |
✗ |
✗ |
|
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\[ {}\left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y = 3 x^{2} \] |
✓ |
✓ |
|
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\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4} = 0 \] |
✓ |
✓ |
|
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\[ {}2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
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\[ {}2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0 \] |
✓ |
✓ |
|
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\[ {}x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9} = 0 \] |
✓ |
✓ |
|
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\[ {}2 x \left (1-x \right ) y^{\prime \prime }+y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
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\[ {}4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}} = 0 \] |
✓ |
✓ |
|
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\[ {}u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0 \] |
✓ |
✓ |
|
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\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0 \] |
✓ |
✓ |
|
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\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0 \] |
✓ |
✓ |
|
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\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0 \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}y^{\prime \prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-6 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }-5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 10 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 16 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 24 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 12 \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 3 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-16 y = 40 \,{\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 6 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 100 \cos \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+12 y = 80 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+25 y = 120 \sin \left (5 x \right ) \] |
✓ |
✓ |
|
|
\[ {}5 y^{\prime \prime }+12 y^{\prime }+20 y = 120 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 30 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 16 \cos \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+17 y = 60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+5 y = 40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+8 y = 30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}5 y^{\prime \prime }+6 y^{\prime }+2 y = x^{2}+6 x \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+y^{\prime } = 2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 12 x \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 16 \,{\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 8 x \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x^{3}-1+2 \cos \left (x \right )+\left (2-4 x \right ) {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{x}+6 x -5 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \sinh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \sin \left (x \right )+4 x \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 4 \,{\mathrm e}^{x}+\left (1-x \right ) \left ({\mathrm e}^{2 x}-1\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 8 x^{4} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x -\frac {1}{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 2 x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 6 \ln \left (x \right ) x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+y = 3 x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 2 x \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2-x \right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (-2+3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}r^{\prime \prime }-6 r^{\prime }+9 r = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 10 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 4 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 26 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 6 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 5 x +4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+13 y^{\prime \prime }-18 y^{\prime }+36 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 6 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -4 y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -4 y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (-1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}z^{\prime \prime }+x z^{\prime }+z = x^{2}+2 x +1 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+2 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-\omega ^{2} x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime \prime }-x^{\prime \prime }+x^{\prime }-x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+42 x^{\prime }+x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x = F \cos \left (\omega t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 16 \cos \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \cosh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x \left (1+x \right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-2 x \right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\frac {y^{\prime }}{2}+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-1+x \right )^{2} y^{\prime \prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 8 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 10 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+25 y = 5 x^{2}+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }-2 y^{\prime }-y = 2 x -3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = 8 \,{\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-7 y^{\prime }-4 y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 54 x +18 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 100 \sin \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 4 \sinh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 2 \cosh \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+10 y = 20-{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \cos \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = x +{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+3 y = x^{2}-1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = {\mathrm e}^{3 x}+\sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+3 x = {\mathrm e}^{-3 t} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 6 \sin \left (t \right ) \] |
✓ |
✓ |
|
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\[ {}x^{\prime \prime }-3 x^{\prime }+2 x = \sin \left (t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 3 \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+6 y^{\prime }+10 y = 50 x \] |
✓ |
✓ |
|
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\[ {}x^{\prime \prime }+2 x^{\prime }+2 x = 85 \sin \left (3 t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime } = 3 \sin \left (x \right )-4 y \] |
✓ |
✓ |
|
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\[ {}\frac {x^{\prime \prime }}{2} = -48 x \] |
✓ |
✓ |
|
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\[ {}x^{\prime \prime }+5 x^{\prime }+6 x = \cos \left (t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-2 y = 4 x^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-2 y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 64 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 50 t^{3}-36 t^{2}-63 t +18 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 2 x \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime } = 9 x^{2}+2 x -1 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-5 y = 2 \,{\mathrm e}^{5 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+y = x^{2}-1 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \cos \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 1+{\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = \frac {{\mathrm e}^{x}}{1+{\mathrm e}^{-x}} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
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\[ {}x^{\prime \prime }+4 x = \sin \left (2 t \right )^{2} \] |
✓ |
✓ |
|
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\[ {}t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N = \ln \left (t \right ) t \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{5}} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-60 y^{\prime }-900 y = 5 \,{\mathrm e}^{10 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-7 y^{\prime } = -3 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = \ln \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-x y^{\prime } = x^{3} {\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y = \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (x -4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = x^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 0 \] |
✓ |
✓ |
|
|
\[ {}q^{\prime \prime }+9 q^{\prime }+14 q = \frac {\sin \left (t \right )}{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+x^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 4-x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 2 \left (1-x \right ) {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = x \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-15 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+12 y^{\prime \prime }-8 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+9 y^{\prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 5 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime } = 5 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = -2 x^{2}+2 x +2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 4 x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \csc \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \csc \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 4 \sec \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = \frac {1}{1+{\mathrm e}^{-x}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = {\mathrm e}^{-x} \sin \left ({\mathrm e}^{-x}\right )+\cos \left ({\mathrm e}^{-x}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y = 2+{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = {\mathrm e}^{x} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = x^{2}+\sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = x +{\mathrm e}^{2 x}-\sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x^{2}+4 x +8 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = -2 \sin \left (x \right )+4 x \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = 2 x^{2}-4 x -1+2 \,{\mathrm e}^{2 x} x^{2}+5 \,{\mathrm e}^{2 x} x +{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{x}+{\mathrm e}^{2 x} x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y = \cos \left (\sqrt {5}\, x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{x}+{\mathrm e}^{-x}+\sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y = x^{3}+x^{2}+{\mathrm e}^{-2 x}+\cos \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-y = {\mathrm e}^{x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 x}}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = x \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{-2 x} \sec \left (x \right )^{2} \left (1+2 \tan \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x +\ln \left (x \right ) x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = \ln \left (x \right )^{2}-\ln \left (x^{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime } = x +\sin \left (\ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y = \ln \left (1+x \right )^{2}+x -1 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y = 6 x \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 2 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 8 \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+\left (2+x \right ) y = \left (x^{2}+2 x +1\right ) {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+\left (x^{2}+3 x +3\right ) y = \left (-x^{2}+6\right ) {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right )^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y = \left (x^{2}-x +1\right ) {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y = \frac {1+x}{x} \] |
✓ |
✓ |
|
|
\[ {}x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-3 y^{\prime }+\frac {3 y}{x} = 2+x \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-\left (3 x +4\right ) y^{\prime }+3 y = \left (3 x +2\right ) {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (9 x^{2}+6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+4 x y = 4 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \frac {-x^{2}+1}{x} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {2}{x^{3}} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = -\frac {2}{x}-\ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime } = x^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y = 8 \] |
✗ |
✗ |
|
|
\[ {}\left (2 x^{3}-1\right ) y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+6 x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+2 y+3 y^{2}\right ) y^{\prime \prime \prime }+6 y^{\prime } \left (y^{\prime \prime }+{y^{\prime }}^{2}+3 y y^{\prime \prime }\right ) = x \] |
✗ |
✓ |
|
|
\[ {}3 x \left (y^{2} y^{\prime \prime \prime }+6 y y^{\prime } y^{\prime \prime }+2 {y^{\prime }}^{3}\right )-3 y \left (y y^{\prime \prime }+2 {y^{\prime }}^{2}\right ) = -\frac {2}{x} \] |
✗ |
✓ |
|
|
\[ {}y y^{\prime \prime \prime }+3 y^{\prime } y^{\prime \prime }-2 y y^{\prime \prime }-2 {y^{\prime }}^{2}+y y^{\prime } = {\mathrm e}^{2 x} \] |
✗ |
✓ |
|
|
\[ {}2 \left (x^{3}+x^{2}\right ) y^{\prime \prime }-\left (-3 x^{2}+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+y^{\prime }-y = 1+x \] |
✓ |
✓ |
|
|
\[ {}2 x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+x y^{\prime }\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} \left (1+x \right ) y^{\prime \prime \prime }-\left (4 x +2\right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}2 x^{2} \left (2-x \right ) y^{\prime \prime }-\left (4-x \right ) x y^{\prime }+\left (-x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) \left (-2+x \right ) y^{\prime \prime }+\left (4 x -6\right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (2+x \right ) y^{\prime \prime }+2 \left (1+x \right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }-3 x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }-y^{\prime }+x^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (2+x \right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (\frac {1}{2}-x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\left (1+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-\left (2-x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+3 y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime }+\lambda y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \] |
✗ |
✗ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-2+x \right )^{2} y^{\prime \prime }+\left (2+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x \left (-1+x \right ) y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+4 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (-2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x \left (1-x \right ) y^{\prime \prime }-\left (6 x +1\right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }-\left (-1+x \right ) y^{\prime }-35 y = 0 \] |
✓ |
✓ |
|
|
\[ {}16 \left (1+x \right )^{2} y^{\prime \prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 10 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {y}{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+5 y = 29 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 21 \,{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 6 t -8 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y}{25} = \frac {t^{2}}{50} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4} = 9 t^{3}+64 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 50 t -100 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -3} \] |
✓ |
✓ |
|
|
\[ {}9 y^{\prime \prime }-6 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-3 t}-{\mathrm e}^{-5 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+10 y^{\prime }+24 y = 144 t^{2} \] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0 |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 4 t & 0 |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = \left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0 |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0 |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0 |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0 |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0 |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \delta \left (t -\pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 4 \delta \left (t -3 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+24 y^{\prime }+37 y = 17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 10 \sin \left (t \right )+10 \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = \delta \left (t -\frac {\pi }{2}\right )+\operatorname {Heaviside}\left (t -\pi \right ) \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = \operatorname {Heaviside}\left (-1+t \right )+\delta \left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (t -\pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}x^{4} y^{\prime \prime \prime \prime }-x^{2} y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 2 x \,{\mathrm e}^{x}-1 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime }+x y^{\prime }-y = \cos \left (\frac {1}{x}\right ) \] |
✓ |
✓ |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }-y = x +\frac {1}{x} \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+\left (-2+x \right ) y^{\prime }-y = x^{2}-1 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\frac {y}{4} = -\frac {x^{2}}{2}+\frac {1}{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}s^{\prime \prime }+2 s^{\prime }+s = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 1+3 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{2 x} x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 4 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u = f \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 4 \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 \sin \left (t \right )-5 \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = g \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-4 y = f \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 50 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 50 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (1+x \right )^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}a^{2} y^{\prime \prime \prime \prime } = y^{\prime \prime } \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 2+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+k^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 1+3 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 i y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (1+4 i\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sin \left (3 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 i y^{\prime }+y = x \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x}+2 x^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = 2 \sin \left (2 x \right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}4 y^{\prime \prime }-y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}6 y^{\prime \prime }+5 y^{\prime }-6 y = x \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+\omega ^{2} y = A \cos \left (\omega x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+6 y^{\prime } = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-i y^{\prime \prime }+4 y^{\prime }-4 i y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-3 i y^{\prime \prime }-3 y^{\prime }+i y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-i y^{\prime \prime }+y^{\prime }-i y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 i y^{\prime }-y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 i y^{\prime }-y = {\mathrm e}^{i x}-2 \,{\mathrm e}^{-i x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-4 y = 3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-2 y = x^{2}+\cos \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+9 y = x^{2} {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = x \,{\mathrm e}^{x} \cos \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+i y^{\prime }+2 y = 2 \cosh \left (2 x \right )+{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y = 0 \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (-1+x \right )^{2} y^{\prime }-\left (-1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\alpha ^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (-2-i\right ) x y^{\prime }+3 i y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 \pi y = x \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (-2+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+k^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-2 y^{\prime } = x^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-k^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 4 x \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-3 y^{\prime } = 5 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-4 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y^{\prime }+20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+2 y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+20 y^{\prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 4 y \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-8 y^{\prime }+7 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-10 y = 6 \,{\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 3 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+10 y^{\prime }+25 y = 14 \,{\mathrm e}^{-5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 25 x^{2}+12 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 20 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 12 x -10 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 6 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 10 x^{4}+2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \tan \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sec \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cot \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cot \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \left (x^{2}-1\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y = x \left (1+x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = {\mathrm e}^{2 x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {x y^{\prime }}{-1+x}+\frac {y}{-1+x} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+48 y^{\prime \prime }+16 y^{\prime }-96 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 10+42 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-5 y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+4 y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+4 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 2 x -1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-y = x \,{\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sec \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = x \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {2}{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \tan \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 3 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = -8 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = x^{2}+2 x +2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \frac {-1+x}{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = -3 \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -3 y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+\left (-x +3\right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \] |
✗ |
✗ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }-3 \left (-1+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 \left (1+x \right )^{2} y^{\prime \prime }-\left (1+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (3 x +5\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = x^{3}-x \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\left (1+x \right ) y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-4 y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+x y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-x y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 5 \,{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-5 y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-2 y = -6 \,{\mathrm e}^{\pi -t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-y = t \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+y = 3 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+3 y = 2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+2 y = t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = t \,{\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[
{}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0 |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\left (1+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-\left (2-x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }-4 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+3 y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{t}+\lambda y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \] |
✗ |
✗ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 10 x^{3}-2 x +5 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sqrt {2}\, \sin \left (\sqrt {2}\, t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime }+3 y^{\prime \prime }-3 y^{\prime }-2 y = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} {\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = {\mathrm e}^{t} \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = t +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (t \right ) \operatorname {Heaviside}\left (t -2 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \operatorname {Heaviside}\left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }-y^{\prime } = 2 t^{2} \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+t y^{\prime }-2 y = 10 \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (t \right )+t \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = \delta \left (t -2 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 1+\delta \left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -2 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = \delta \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime } = y^{\prime }+x^{5} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\beta ^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime }-x^{2} y^{\prime } = -x^{2}+3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = -\cos \left (x \right ) \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 12 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = x^{2}+2 x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (4 x^{2}+1\right ) y^{\prime \prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+10 x y^{\prime }+20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-9\right ) y^{\prime \prime }+3 x y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+3 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+9 x y^{\prime }-36 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+3 x y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (9 x^{2}+1\right ) y^{\prime \prime }-18 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (3 x^{2}+1\right ) y^{\prime \prime }+13 x y^{\prime }+7 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+11 x y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-2 x +2\right ) y^{\prime \prime }-4 \left (-1+x \right ) y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x \left (1+x \right ) y^{\prime \prime }+3 \left (1+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (4 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (1+7 x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x \left (x +3\right ) y^{\prime \prime }-3 \left (1+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+\left (-2 x^{2}+1\right ) y^{\prime }-4 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (4-x \right ) y^{\prime \prime }+\left (2-x \right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-3 x \left (1-x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x \left (4 x -1\right ) y^{\prime }+2 \left (3 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (1+3 x \right ) y^{\prime }+\left (1-6 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-1+x \right ) y^{\prime }+\left (1-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-2+x \right ) y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-2+x \right ) y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 \left (x -4\right )^{2} y^{\prime \prime }+\left (x -4\right ) \left (x -8\right ) y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x \left (1+x \right ) y^{\prime }+\left (1-3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x \left (-2+x \right ) y^{\prime }+2 \left (2-3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+2 x \left (6 x +1\right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (5+x \right ) y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (5+x \right ) y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (3 x +4\right ) y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (x +3\right ) y^{\prime \prime }-9 y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-2 x \right ) y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (x^{3}-1\right ) y^{\prime }+x^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (4 x -1\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+2 x \left (2-x \right ) y^{\prime }-\left (1+3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (-x +3\right ) y^{\prime }-5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-\left (6 x^{2}-3 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-2+x \right )^{2} y^{\prime \prime }-2 \left (-2+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-2+x \right )^{2} y^{\prime \prime }-2 \left (-2+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x \left (2 x +7\right ) y^{\prime }+2 \left (5+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (x^{2}+3\right ) y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }-18 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime \prime }-\left (x^{2}+7\right ) y^{\prime }+4 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (1+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-2 x \left (2+x \right ) y^{\prime }+\left (x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x^{2}-3\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (1+3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+2 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime \prime }+5 \left (-x^{2}+1\right ) y^{\prime }-4 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (2 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-2 x \right ) y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+18 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 4 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}5 y^{\prime \prime }+2 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+4 y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+4 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }+4 y^{\prime } = t^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-2 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }-y^{\prime }+4 t^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = f \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = k \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 4 \sin \left (x \right )-4 \] |
✓ |
✓ |
|
|
\[ {}z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-2 x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-3 x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{2}-x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{3}+2 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{4}-6 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{5}+24 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+c y^{\prime }+k y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = x \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = x \] |
✗ |
✗ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+y = 8 \sqrt {x}\, \left (1+\ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-x y = x^{2}+2 x \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (1+x \right ) y^{\prime }-\left (1-4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+3 x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}+6 x \right ) y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-9 x y^{\prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \left (x^{2}+3\right ) y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+20 y^{\prime }+500 y = 100000 \cos \left (100 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y = 6 x^{3} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {1}{x} \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \frac {1}{x} \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }+y = \frac {1}{x} \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \frac {1}{x} \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-24 y = 16-\left (2+x \right ) {\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = {\mathrm e}^{\cos \left (x \right ) a} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}a y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = 1+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = x^{2}+x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = x^{3}+x^{2}+x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 1+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x^{2}+x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x^{3}+x^{2}+x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 1+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x^{2}+x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x^{3}+x^{2}+x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {2 y}{x^{2}} = x \,{\mathrm e}^{-\sqrt {x}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}} = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-c^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 2 x^{3}-x^{2} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 8 x^{3} \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = x^{1+m} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y = {\mathrm e}^{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 \left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y = x \,{\mathrm e}^{x}+3 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-t \left (2+t \right ) y^{\prime }+\left (2+t \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (2+x \right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (4+6 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }-9 x y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (-2+x \right ) y^{\prime }+36 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (1+x \right ) y^{\prime }+60 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+3 x \right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x +4\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (1+x \right ) y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (4 x +2\right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}12 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}18 x^{2} \left (1+x \right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x \left (5+x \right ) y^{\prime }-\left (2-3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-2 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-\left (1+3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2+x \right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} \left (1+x \right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (1+x \right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} \left (1+x \right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (-x +3\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 x y^{\prime }+\left (1+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (3+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (4-3 x \right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (2+x \right ) y^{\prime }-\left (2-3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-3 \left (x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+2 t \right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }-\left (4+t \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }+t y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f = 0 \] |
✓ |
✓ |
|
|
\[ {}z y^{\prime \prime }-2 y^{\prime }+y z = 0 \] |
✓ |
✓ |
|
|
\[ {}z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }-x \left (x +8\right ) y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x \left (2+x \right ) y^{\prime }+2 \left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-4 x \right ) y^{\prime \prime }-\frac {x y^{\prime }}{2}-\frac {3 x y}{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }+\left (3 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9} = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0 \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0 \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0 \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0 \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1+x \right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-1+x \right )^{2} y^{\prime \prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+x^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+x y^{\prime }\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}2 \left (2-x \right ) x^{2} y^{\prime \prime }-x \left (4-x \right ) y^{\prime }+\left (-x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (2+x \right ) y^{\prime \prime }+2 \left (1+x \right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (2+x \right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime }+\lambda y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x \left (-1+x \right ) y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+4 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (-2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+\left (-2+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {u}{x^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (1+x \right )^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y}{2 x^{4}} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \left (x^{2}+3\right ) y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime }+y^{\prime }-\frac {y}{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-\left (2+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-t \left (2+t \right ) y^{\prime }+\left (2+t \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-t \left (2+t \right ) y^{\prime }+\left (2+t \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x \left (-1+x \right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+\left (1+4 x \right ) y^{\prime }+\left (2 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (-2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (2+x \right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (4+6 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (-2+x \right ) y^{\prime }+36 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (1+x \right ) y^{\prime }+60 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+3 x \right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x +4\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (1+x \right ) y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (4 x +2\right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 x y^{\prime }+\left (2 x^{2}+5\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}12 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}18 x^{2} \left (1+x \right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x \left (5+x \right ) y^{\prime }-\left (2-3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (1-2 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-\left (1+3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2+x \right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} \left (1+x \right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (1+x \right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y = 0 \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} \left (1+x \right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (-x +3\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 x y^{\prime }+\left (1+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (3+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (4-3 x \right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (2+x \right ) y^{\prime }-\left (2-3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-3 \left (x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+2 t \right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }-\left (4+t \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }+t y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f = 0 \] |
✓ |
✓ |
|
|
\[ {}z y^{\prime \prime }-2 y^{\prime }+y z = 0 \] |
✓ |
✓ |
|
|
\[ {}z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z} = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }-x \left (x +8\right ) y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x \left (2+x \right ) y^{\prime }+2 \left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {9}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (-\frac {1}{4} x -x^{2}\right ) y^{\prime }-\frac {5 x y}{16} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }+\left (3 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9} = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0 \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0 \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0 \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0 \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2-x \right ) x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (-2+3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1+x \right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-1+x \right )^{2} y^{\prime \prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+x^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+x y^{\prime }\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}2 \left (2-x \right ) x^{2} y^{\prime \prime }-x \left (4-x \right ) y^{\prime }+\left (-x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (2+x \right ) y^{\prime \prime }+2 \left (1+x \right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (2+x \right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime }+\lambda y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
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\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
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\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
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\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0 \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
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\[ {}2 x \left (-1+x \right ) y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }+2 y^{\prime }+4 x y = 0 \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (-2+x \right ) y = 0 \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0 \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
✓ |
✓ |
|
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\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
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\[ {}4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
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\[ {}2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
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\[ {}3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0 \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0 \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4} = 0 \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0 \] |
✓ |
✓ |
|
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\[ {}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
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\[ {}2 x y^{\prime \prime }+\left (-2+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0 \] |
✓ |
✓ |
|
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\[ {}u^{\prime \prime }+2 u^{\prime }+u = 0 \] |
✓ |
✓ |
|
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\[ {}u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y = 0 \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (1+x \right )^{2}} = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \left (x^{2}+3\right ) y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {2 y}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {6 y}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (-1+x \right )^{2}}+\frac {3}{16 x \left (-1+x \right )}\right ) y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {20 y}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {12 y}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {y}{4 x^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y}{x^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {\left (4 x^{6}-8 x^{5}+12 x^{4}+4 x^{3}+7 x^{2}-20 x +4\right ) y}{4 x^{4}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \left (\frac {6}{x^{2}}-1\right ) y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \left (\frac {1}{x}-\frac {3}{16 x^{2}}\right ) y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (-1+x \right )^{2}}+\frac {3}{16 x \left (-1+x \right )}\right ) y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (5 x^{2}+27\right ) y}{36 \left (x^{2}-1\right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {y}{4 x^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \left (x^{2}+3\right ) y \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime } = 2 y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-2+x \right )^{2} y^{\prime \prime }-\left (-2+x \right ) y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y-\sin \left (n x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y-a \cos \left (b x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y-\sin \left (x a \right ) \sin \left (b x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y-4 x^{2} {\mathrm e}^{x^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a^{2} y-\cot \left (x a \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+l y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+b y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+b y-f \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+\left (-1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y-{\mathrm e}^{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y-{\mathrm e}^{x^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 a x y^{\prime }+a^{2} x^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-\left (1+x \right )^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} \left (1+x \right ) y^{\prime }+x \left (x^{4}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x^{4} y^{\prime }-x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+\tan \left (x \right )+b y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (y^{\prime \prime }+y\right )-\cos \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }-y a \,x^{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }-x y-{\mathrm e}^{x} = 0 \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }+2 y^{\prime }+a x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-x y^{\prime }-y-x \left (1+x \right ) {\mathrm e}^{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (1+x \right ) y^{\prime }-2 \left (-1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-2 \left (x a +b \right ) y^{\prime }+\left (x \,a^{2}+2 a b \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (x^{2}-x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (x^{2}-x -2\right ) y^{\prime }-x \left (x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x^{2} a +1\right ) y^{\prime }+b \,x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (4 x^{2}-1\right ) y^{\prime }-4 x^{3} y-4 x^{5} = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (2 a \,x^{3}-1\right ) y^{\prime }+\left (a^{2} x^{3}+a \right ) x^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+y^{\prime }+a y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x -1\right ) y^{\prime \prime }-\left (3 x -4\right ) y^{\prime }+\left (x -3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x y^{\prime \prime }+2 y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x y^{\prime \prime }+4 y^{\prime }-\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}a x y^{\prime \prime }+\left (b x +3 a \right ) y^{\prime }+3 b y = 0 \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+a y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x^{2} a +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (a^{2} x^{2}-6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+a y^{\prime }-\left (b^{2} x^{2}+a b \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y-x^{2} a = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+a y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x +a \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y-3 x^{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y-x^{5} \ln \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y-x \sin \left (x \right )-\left (x^{2} a +12 a +4\right ) \cos \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y-\frac {x^{2}}{\cos \left (x \right )} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y-\frac {x^{3}}{\cos \left (x \right )} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (a^{2} x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y-5 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y-\ln \left (x \right ) x^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y-x^{4}+x^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y-\sin \left (x \right ) x^{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+a x y^{\prime }+b y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }+\left (x -9\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }+\left (3 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (-1+x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x^{2}-2 x \right ) y^{\prime }-\left (3 x +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (a +2 b \right ) x^{2} y^{\prime }+\left (\left (a +b \right ) b \,x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}+2\right ) x y^{\prime }+\left (x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (4 x^{4}+2 x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+a y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+a y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-2 \cos \left (x \right )+2 x = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+a x y^{\prime }+\left (a -2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+2 = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+a y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-a = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-\left (1+3 x \right ) y^{\prime }-\left (x^{2}-x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 \left (v -1\right ) x y^{\prime }-2 v y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 a x y^{\prime }+a \left (a -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-a^{2}+x^{2}\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+x -2\right ) y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }-\left (6 x^{2}+7 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+a y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+\left (\left (1+a \right ) x +b \right ) y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+\left (\left (\operatorname {a1} +\operatorname {b1} +1\right ) x -\operatorname {d1} \right ) y^{\prime }+\operatorname {a1} \operatorname {b1} \operatorname {d1} = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }+\left (x^{2}+x -1\right ) y^{\prime }-\left (2+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{\frac {7}{3}} = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+3 x +4\right ) y^{\prime \prime }+\left (x^{2}+x +1\right ) y^{\prime }-\left (2 x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-2+x \right )^{2} y^{\prime \prime }-\left (-2+x \right ) y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-\left (2 x^{2}+l -5 x \right ) y^{\prime }-\left (4 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+6 x +4\right ) y^{\prime \prime }+\left (10 x^{2}+21 x +8\right ) y^{\prime }+\left (12 x^{2}+17 x +8\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (4 x^{2}+1\right ) y-4 \sqrt {x^{3}}\, {\mathrm e}^{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (x^{2} a +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+5 x y^{\prime }-y-\ln \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }-\left (4 x^{2}+12 x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x \left (2 x -1\right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+6\right ) \left (x^{2}-4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y-3 x -1 = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (4 x -1\right ) y^{\prime \prime }+\left (\left (4 a +2\right ) x -a \right ) y^{\prime }+a \left (a -1\right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}\left (3 x -1\right )^{2} y^{\prime \prime }+3 \left (3 x -1\right ) y^{\prime }-9 y-\ln \left (3 x -1\right )^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x \left (-1+x \right ) y^{\prime \prime }+3 \left (2 x -1\right ) y^{\prime }-20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}16 x^{2} y^{\prime \prime }+\left (3+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }-\left (5+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (27 x^{2}+4\right ) y^{\prime \prime }+27 x y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}50 x \left (-1+x \right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2} a +1\right ) y^{\prime \prime }+a x y^{\prime }+b y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime }-2 a^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2} a +b x \right ) y^{\prime \prime }+2 b y^{\prime }-2 a y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime }+x y^{\prime }-\left (2 x +3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime }-x^{2} y^{\prime }+x y-\ln \left (x \right )^{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }+x y-1 = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+2 \left (x^{2}-1\right ) y^{\prime }-2 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime }+y a \,x^{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime }-6 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (x^{2}-2\right ) y^{\prime \prime }-\left (x^{3}+3 x^{2}-2 x -2\right ) y^{\prime }+\left (x^{2}+4 x +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+2 x \left (3 x +2\right ) y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {2 \left (-2+x \right ) y^{\prime }}{x \left (-1+x \right )}+\frac {2 \left (1+x \right ) y}{x^{2} \left (-1+x \right )} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {\left (5 x -4\right ) y^{\prime }}{x \left (-1+x \right )}-\frac {\left (9 x -6\right ) y}{x^{2} \left (-1+x \right )} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {y^{\prime }}{1+x}-\frac {y}{x \left (1+x \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {2 y}{x \left (-1+x \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {\left (x -4\right ) y^{\prime }}{2 x \left (-2+x \right )}-\frac {\left (x -3\right ) y}{2 x^{2} \left (-2+x \right )} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {y^{\prime }}{1+x}-\frac {\left (1+3 x \right ) y}{4 x^{2} \left (1+x \right )} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (1-3 x \right ) y}{\left (-1+x \right ) \left (2 x -1\right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (3 x +a +2 b \right ) y^{\prime }}{2 \left (x +a \right ) \left (x +b \right )}-\frac {\left (-b +a \right ) y}{4 \left (x +a \right )^{2} \left (x +b \right )} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {\left (6 x -1\right ) y^{\prime }}{3 x \left (-2+x \right )}+\frac {y}{3 x^{2} \left (-2+x \right )} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {2 \left (x a +2 b \right ) y^{\prime }}{x \left (x a +b \right )}-\frac {\left (2 x a +6 b \right ) y}{\left (x a +b \right ) x^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {a y}{x^{4}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {y^{\prime }}{x^{3}}+\frac {2 y}{x^{4}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {\left (a +b \right ) y^{\prime }}{x^{2}}-\frac {\left (x \left (a +b \right )+a b \right ) y}{x^{4}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {2 y^{\prime }}{x}-\frac {a^{2} y}{x^{4}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x^{3}}+\frac {y}{x^{4}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {2 \left (x +a \right ) y^{\prime }}{x^{2}}-\frac {b y}{x^{4}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {\left (2 x^{2}-1\right ) y^{\prime }}{x^{3}}-\frac {y}{x^{4}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {\left (2 x^{2}-1\right ) y^{\prime }}{x^{3}}-\frac {2 y}{x^{4}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (x^{3}-1\right ) y^{\prime }}{x \left (x^{3}+1\right )}+\frac {x y}{x^{3}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {\left (x^{2}-2\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (x^{2}-2\right ) y}{x^{2} \left (x^{2}-1\right )} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (a \left (1+a \right )-a \,x^{2} \left (a +3\right )\right ) y}{x^{2} \left (x^{2}-1\right )} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {a y}{\left (x^{2}+1\right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {2 x y^{\prime }}{x^{2}+1}-\frac {y}{\left (x^{2}+1\right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {a y}{\left (x^{2}-1\right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {2 x y^{\prime }}{x^{2}-1}+\frac {a^{2} y}{\left (x^{2}-1\right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (2 x^{2}+a \right ) y^{\prime }}{x \left (x^{2}+a \right )}-\frac {b y}{x^{2} \left (x^{2}+a \right )} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {b^{2} y}{\left (a^{2}+x^{2}\right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {2 \left (x^{2}-1\right ) y^{\prime }}{x \left (-1+x \right )^{2}}-\frac {\left (-2 x^{2}+2 x +2\right ) y}{x^{2} \left (-1+x \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {12 y}{\left (1+x \right )^{2} \left (x^{2}+2 x +3\right )} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {b y}{x^{2} \left (x -a \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {b y}{x^{2} \left (x -a \right )^{2}}+c \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {c y}{\left (x -a \right )^{2} \left (-b +x \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (\left (\alpha +\beta +1\right ) \left (x -a \right )^{2} \left (-b +x \right )+\left (1-\alpha -\beta \right ) \left (-b +x \right )^{2} \left (x -a \right )\right ) y^{\prime }}{\left (x -a \right )^{2} \left (-b +x \right )^{2}}-\frac {\alpha \beta \left (-b +a \right )^{2} y}{\left (x -a \right )^{2} \left (-b +x \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (x^{2} a +a -3\right ) y}{4 \left (x^{2}+1\right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {18 y}{\left (2 x +1\right )^{2} \left (x^{2}+x +1\right )} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {3 y}{4 \left (x^{2}+x +1\right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {3 y}{16 x^{2} \left (-1+x \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {\left (7 x^{2} a +5\right ) y^{\prime }}{x \left (x^{2} a +1\right )}-\frac {\left (15 x^{2} a +5\right ) y}{x^{2} \left (x^{2} a +1\right )} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {2 y^{\prime }}{x}-\frac {c y}{x^{2} \left (x a +b \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {y}{\left (x a +b \right )^{4}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {A y}{\left (x^{2} a +b x +c \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {y^{\prime }}{x^{4}}+\frac {y}{x^{5}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {\left (1+3 x \right ) y^{\prime }}{\left (-1+x \right ) \left (1+x \right )}-\frac {36 \left (1+x \right )^{2} y}{\left (-1+x \right )^{2} \left (3 x +5\right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {y^{\prime }}{x}-\frac {a y}{x^{6}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (3 x^{2}+a \right ) y^{\prime }}{x^{3}}-\frac {b y}{x^{6}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {\left (-2 x^{2}+1\right ) y}{4 x^{6}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {\left (2 x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {\left (a \,x^{4}+10 x^{2}+1\right ) y}{4 x^{6}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {27 x y}{16 \left (x^{3}-1\right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {y^{\prime }}{x}-\frac {\left (-1+x \right ) y}{x^{4}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {y^{\prime }}{x}-\frac {\left (-x -1\right ) y}{x^{4}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {b^{2} y}{\left (-a^{2}+x^{2}\right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+\left (a +b -1\right ) x y^{\prime }-y a b = 0 \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-a^{2} y^{\prime }+2 a^{2} y-\sinh \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-a^{3} y-{\mathrm e}^{x a} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+\operatorname {a2} y^{\prime \prime }+\operatorname {a1} y^{\prime }+\operatorname {a0} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+f \left (x \right ) \left (x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y\right ) = 0 \] |
✗ |
✗ |
|
|
\[ {}4 y^{\prime \prime \prime }-8 y^{\prime \prime }-11 y^{\prime }-3 y+18 \,{\mathrm e}^{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime } x +\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-f \left (x \right ) = 0 \] |
✗ |
✗ |
|
|
\[ {}\left (-2+x \right ) x y^{\prime \prime \prime }-\left (-2+x \right ) x y^{\prime \prime }-2 y^{\prime }+2 y = 0 \] |
✗ |
✗ |
|
|
\[ {}\left (2 x -1\right ) y^{\prime \prime \prime }+\left (x +4\right ) y^{\prime \prime }+2 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-x y^{\prime \prime }+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime }-\ln \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime }+6 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-2 \left (n +1\right ) x y^{\prime \prime }+\left (x^{2} a +6 n \right ) y^{\prime }-2 a x y = 0 \] |
✗ |
✗ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime \prime }+8 x y^{\prime \prime }+10 y^{\prime }-3+\frac {1}{x^{2}}-2 \ln \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime \prime }-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }-2 x y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y-6 x^{3} \left (-1+x \right ) \ln \left (x \right )+x^{3} \left (x +8\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+\left (-a^{2}+1\right ) x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+\left (x^{2}+8\right ) x y^{\prime }-2 \left (x^{2}+4\right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+\left (x +3\right ) x^{2} y^{\prime \prime }+5 \left (x -6\right ) x y^{\prime }+\left (4 x +30\right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+\ln \left (x \right )+2 x y^{\prime }-y-2 x^{3} = 0 \] |
✓ |
✗ |
|
|
\[ {}\left (x^{2}+1\right ) x y^{\prime \prime \prime }+3 \left (2 x^{2}+1\right ) y^{\prime \prime }-12 y = 0 \] |
✗ |
✗ |
|
|
\[ {}\left (x +3\right ) x^{2} y^{\prime \prime \prime }-3 x \left (2+x \right ) y^{\prime \prime }+6 \left (1+x \right ) y^{\prime }-6 y = 0 \] |
✗ |
✗ |
|
|
\[ {}\left (1+x \right ) x^{3} y^{\prime \prime \prime }-\left (4 x +2\right ) x^{2} y^{\prime \prime }+\left (10 x +4\right ) x y^{\prime }-4 \left (1+3 x \right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}4 x^{4} y^{\prime \prime \prime }-4 x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }-1 = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) x^{3} y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-4 \left (3 x^{2}+1\right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{6} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y = 0 \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime \prime \prime }-12 y^{\prime \prime }+12 y-16 x^{4} {\mathrm e}^{x^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y-\cosh \left (x a \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+\left (\lambda +1\right ) a^{2} y^{\prime \prime }+\lambda \,a^{4} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y-32 \sin \left (2 x \right )+24 \cos \left (2 x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+11 y^{\prime \prime }-3 y^{\prime }-4 \cos \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime } x +2 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime } x +6 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime } x +6 y^{\prime \prime }-\lambda ^{2} y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime } x +12 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime } x +12 y^{\prime \prime }-\lambda ^{2} y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }+\left (2 n -2 \nu +4\right ) x y^{\prime \prime \prime }+\left (n -\nu +1\right ) \left (n -\nu +2\right ) y^{\prime \prime }-\frac {b^{4} y}{16} = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{3} y^{\prime \prime \prime \prime }+2 x^{2} y^{\prime \prime \prime }-x y^{\prime \prime }+y^{\prime }-a^{4} x^{3} y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }+\left (4 n^{2}-1\right ) x y^{\prime }-4 x^{4} y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }-\left (4 n^{2}-1\right ) x y^{\prime }+\left (-4 x^{4}+4 n^{2}-1\right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }+a y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \,{\mathrm e}^{x} y^{\prime }+{\mathrm e}^{x} y-\frac {1}{x^{5}} = 0 \] |
✗ |
✗ |
|
|
\[ {}f \left (y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y\right )+2 \operatorname {df} \left (y^{\prime \prime \prime }-a^{2} y^{\prime }\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a^{3} x \left (-x a +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+b y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2}+x a +1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+b x \left (-b \,x^{3}+x a +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (x a +b \right ) y^{\prime }-a y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+a y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+c \left (x a +b -c \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (x a +2 b \right ) y^{\prime }+\left (a b x +b^{2}-a \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{2}+b x +1\right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }+2 \left (x a +b \right ) y^{\prime }+\left (a^{2} x^{2}+2 a b x +c \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a \left (-b^{2}+x^{2}\right ) y^{\prime }-a \left (x +b \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (x^{2} a +b \right ) y^{\prime }+c \left (x^{2} a +b -c \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (x^{2} a +2 b \right ) y^{\prime }+\left (a b \,x^{2}-x a +b^{2}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (2 x^{2}+a \right ) y^{\prime }+\left (x^{4}+x^{2} a +b +2 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (a b \,x^{2}+b x +2 a \right ) y^{\prime }+a^{2} \left (b \,x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (x^{2} a +b x +c \right ) y^{\prime }+x \left (a b \,x^{2}+b c +2 a \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (x^{2} a +b x +c \right ) y^{\prime }+\left (a b \,x^{3}+a c \,x^{2}+b \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (a \,x^{3}+2 b \right ) y^{\prime }+\left (a b \,x^{3}-x^{2} a +b^{2}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (a \,x^{3}+b x \right ) y^{\prime }+2 \left (2 x^{2} a +b \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (a b \,x^{3}+b \,x^{2}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{3}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\frac {y^{\prime }}{2}+a y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+a x y^{\prime }+a y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+c \left (\left (a -c \right ) x +b \right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}x y^{\prime \prime }+\left (2 x a +b \right ) y^{\prime }+a \left (x a +b \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (x a +1\right ) y^{\prime }-b \,x^{2} \left (b x +a \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x a +1\right ) y^{\prime }+\left (b \,x^{3}+x \,a^{2}+a \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+c x \left (-c \,x^{2}+x a +b +1\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (a b \,x^{2}+b -5\right ) y^{\prime }+2 a^{2} \left (b -2\right ) x^{3} y = 0 \] |
✗ |
✗ |
|
|
\[ {}x y^{\prime \prime }+\left (x^{2} a +b x \right ) y^{\prime }-\left (a c \,x^{2}+\left (b c +c^{2}+a \right ) x +b +2 c \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (x^{2} a +b x +2\right ) y^{\prime }+b y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (x^{2} a +b x +c \right ) y^{\prime }+\left (2 x a +b \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (x^{2} a +b x +c \right ) y^{\prime }+\left (c -1\right ) \left (x a +b \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (a \,x^{3}+b \right ) y^{\prime }+a \left (b -1\right ) x^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+x \left (x^{2} a +b \right ) y^{\prime }+\left (3 x^{2} a +b \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (a \,x^{3}+b \,x^{2}+2\right ) y^{\prime }+b x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (a b \,x^{3}+b \,x^{2}+x a -1\right ) y^{\prime }+a^{2} b \,x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime }+\left (d -1\right ) \left (x^{2} a +b x +c \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x +a \right ) y^{\prime \prime }+\left (b x +c \right ) y^{\prime }+b y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x a +b \right ) y^{\prime \prime }+s \left (c x +d \right ) y^{\prime }-s^{2} \left (\left (a +c \right ) x +b +d \right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{2} y^{\prime \prime }+a y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (a^{2} x^{2}+2 a b x +b^{2}-b \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (a \,x^{3}+\frac {5}{16}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (a^{2} x^{4}+a \left (2 b -1\right ) x^{2}+b \left (b +1\right )\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+a x y^{\prime }+b y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-\left (a^{2} x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 a x y^{\prime }+\left (b^{2} x^{2}+a \left (1+a \right )\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 a x y^{\prime }+\left (-b^{2} x^{2}+a \left (1+a \right )\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2} a +b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{2}+b \right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2} a +b x \right ) y^{\prime }-b y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2} a +b x \right ) y^{\prime }+\left (k \left (a -k \right ) x^{2}+\left (a n +b k -2 k n \right ) x +n \left (b -n -1\right )\right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2} a +\left (a b -1\right ) x +b \right ) y^{\prime }+a^{2} b x y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-a^{2}+x^{2}\right ) y^{\prime \prime }+b y^{\prime }-6 y = 0 \] |
✗ |
✗ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+a y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+n^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-3 x y^{\prime }+n \left (n +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2} a +b \right ) y^{\prime \prime }+a x y^{\prime }+c y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+a \right ) y^{\prime \prime }+2 b x y^{\prime }+2 \left (b -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-a^{2}+x^{2}\right ) y^{\prime \prime }+2 b x y^{\prime }+b \left (b -1\right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime \prime }+2 b x y^{\prime }+b \left (b -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2} a +b \right ) y^{\prime \prime }+\left (c \,x^{2}+d \right ) y^{\prime }+\lambda \left (\left (-a \lambda +c \right ) x^{2}+d -b \lambda \right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}\left (x^{2} a +b \right ) y^{\prime \prime }+\left (\lambda \left (a +c \right ) x^{2}+\left (c -a \right ) x +2 b \lambda \right ) y^{\prime }+\lambda ^{2} \left (c \,x^{2}+b \right ) y = 0 \] |
✗ |
✗ |
|
|
|
|||
|
\[ {}\left (2 x a +x^{2}+b \right ) y^{\prime \prime }+\left (x +a \right ) y^{\prime }-m^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2} a +b x +c \right ) y^{\prime \prime }+\left (d x +k \right ) y^{\prime }+\left (d -2 a \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2} a +b x +c \right ) y^{\prime \prime }+\left (k x +d \right ) y^{\prime }-k y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2} a +2 b x +c \right ) y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+d y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2} a +2 b x +c \right ) y^{\prime \prime }+3 \left (x a +b \right ) y^{\prime }+d y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2} a +b x +c \right ) y^{\prime \prime }-\left (-k^{2}+x^{2}\right ) y^{\prime }+\left (x +k \right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}\left (x^{2} a +b x +c \right ) y^{\prime \prime }+\left (k^{3}+x^{3}\right ) y^{\prime }-\left (k^{2}-k x +x^{2}\right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{3} y^{\prime \prime }+\left (x^{2} a +b x \right ) y^{\prime }+b y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{3} y^{\prime \prime }+\left (a \,x^{3}+a b x -x^{2}+b \right ) y^{\prime }+a^{2} b x y = 0 \] |
✗ |
✗ |
|
|
\[ {}x \left (x^{2} a +b \right ) y^{\prime \prime }+2 \left (x^{2} a +b \right ) y^{\prime }-2 a x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x a +b \right ) y^{\prime \prime }+\left (c \,x^{2}+\left (a \lambda +2 b \right ) x +b \lambda \right ) y^{\prime }+\lambda \left (c -2 a \right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{2} \left (x a +b \right ) y^{\prime \prime }-2 x \left (x a +2 b \right ) y^{\prime }+2 \left (x a +3 b \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x a +b \right ) y^{\prime \prime }+\left (a \left (2-n -m \right ) x^{2}-b \left (m +n \right ) x \right ) y^{\prime }+\left (a m \left (n -1\right ) x +b n \left (1+m \right )\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\beta x +2 c \right ) y^{\prime }+\left (\beta -2 b \right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\beta x +2 c \right ) y^{\prime }-\left (\alpha x +2 b -\beta \right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (-2 x^{2} a -\left (b +1\right ) x +k \right ) y^{\prime }+2 \left (x a +1\right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (\left (m -a \right ) x^{2}+\left (2 c m -1\right ) x -c \right ) y^{\prime }+\left (-2 m x +1\right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}\left (a \,x^{3}+x^{2}+b \right ) y^{\prime \prime }+a^{2} x \left (x^{2}-b \right ) y^{\prime }-a^{3} b x y = 0 \] |
✗ |
✗ |
|
|
\[ {}2 x \left (x^{2} a +b x +c \right ) y^{\prime \prime }+\left (x^{2} a -c \right ) y^{\prime }+\lambda \,x^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }-\left (-\lambda ^{2}+x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (3 x^{2} a +2 b x +c \right ) y^{\prime }+\lambda y = 0 \] |
✓ |
✗ |
|
|
\[ {}2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+3 \left (3 x^{2} a +2 b x +c \right ) y^{\prime }+\left (6 x a +2 b +\lambda \right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (\lambda ^{3}+x^{3}\right ) y^{\prime }-\left (\lambda ^{2}-\lambda x +x^{2}\right ) y = 0 \] |
✗ |
✗ |
|
|
\[ {}x^{4} y^{\prime \prime }+a y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime }-\left (a +b \right ) x^{2} y^{\prime }+\left (x \left (a +b \right )+a b \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime }+2 x^{2} \left (x +a \right ) y^{\prime }+b y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x -a \right )^{2} y^{\prime \prime }+b y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x -a \right )^{2} y^{\prime \prime }+b y = c \,x^{2} \left (x -a \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right )^{2} y^{\prime \prime }+a y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right )^{2} y^{\prime \prime }+a y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (a^{2}+x^{2}\right )^{2} y^{\prime \prime }+b^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-a^{2}+x^{2}\right )^{2} y^{\prime \prime }+b^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 \left (x^{2}+1\right )^{2} y^{\prime \prime }+\left (x^{2} a +a -3\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2} a +b \right )^{2} y^{\prime \prime }+2 a x \left (x^{2} a +b \right ) y^{\prime }+c y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2} a +b \right )^{2} y^{\prime \prime }+\left (2 x a +c \right ) \left (x^{2} a +b \right ) y^{\prime }+k y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2} a +b \right )^{2} y^{\prime \prime }+\left (x^{2} a +b \right ) \left (c \,x^{2}+d \right ) y^{\prime }+2 \left (-a d +b c \right ) x y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x -a \right )^{2} \left (-b +x \right )^{2} y^{\prime \prime }-c y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x -a \right )^{2} \left (-b +x \right )^{2} y^{\prime \prime }+\left (x -a \right ) \left (-b +x \right ) \left (2 x +\lambda \right ) y^{\prime }+\mu y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2} a +b x +c \right )^{2} y^{\prime \prime }+y A = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2} a +b x +c \right )^{2} y^{\prime \prime }+\left (2 x a +k \right ) \left (x^{2} a +b x +c \right ) y^{\prime }+m y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{6} y^{\prime \prime }-x^{5} y^{\prime }+a y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{6} y^{\prime \prime }+\left (3 x^{2}+a \right ) x^{3} y^{\prime }+b y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{{\mathrm e}^{x}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 2 \,{\mathrm e}^{-x}-{\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = x^{2}+\cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \,{\mathrm e}^{2 x} x -\sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \,{\mathrm e}^{x}+x^{3}-x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{2 x}-\cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime } = 3 x^{2}+\sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = {\mathrm e}^{x}+4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{2 x}+1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y = 10 x +\frac {10}{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }-\left (1+x \right ) y^{\prime }+6 y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \cos \left (x \right )-{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 x^{3}-x \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (1+\ln \left (x \right )\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = x^{2}-x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sec \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {1}{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = x \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = x^{2}-x -1 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }-x y = 2 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y = \frac {1}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-8 x^{3} y = 4 x^{3} {\mathrm e}^{-x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (-x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{3}-1\right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime } = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime \prime } x -y^{\prime \prime }-x y^{\prime }+y = -x^{2}+1 \] |
✗ |
✗ |
|
|
\[ {}\left (2+x \right )^{2} y^{\prime \prime \prime }+\left (2+x \right ) y^{\prime \prime }+y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }+4 \left (-1+x \right ) y^{\prime }+2 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-5 x y^{\prime \prime }+\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y = 0 \] |
✗ |
✗ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 2 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+18 x y^{\prime }+6 y = 0 \] |
✗ |
✗ |
|
|
\[ {}\left (x^{2}-x \right ) y^{\prime \prime }+\left (4 x +2\right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+2 x^{\prime }+2 x = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} x^{\prime \prime }-6 x = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{\prime \prime }-5 x^{\prime }-3 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime } = -3 \sqrt {t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime }+t x^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}\frac {x^{\prime }+t x^{\prime \prime }}{t} = -2 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime } = 3 t \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-4 x^{\prime }+4 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-2 x^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+3 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-4 x^{\prime }+4 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-2 x^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+3 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+4 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-4 x^{\prime }+6 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+9 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-12 x = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{\prime \prime }+3 x^{\prime }+3 x = 0 \] |
✓ |
✓ |
|
|
\[ {}\frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\frac {x^{\prime }}{8}+x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = 3 t^{3}-1 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = 3 \cos \left (t \right )-2 \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = 12 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = t^{2} {\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (7 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = {\mathrm e}^{2 t} \cos \left (t \right )+t^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = t \,{\mathrm e}^{-t} \sin \left (\pi t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = \left (2+t \right ) \sin \left (\pi t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = 4 t +5 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (2 t \right )+t \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = t^{3}+1-4 t \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = -6+2 \,{\mathrm e}^{2 t} \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+7 x = t \,{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-x^{\prime } = 6+{\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = t^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-3 x^{\prime }-4 x = 2 t^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = 9 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-4 x = \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+2 x = t \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-b x^{\prime }+x = \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-3 x^{\prime }-40 x = 2 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-2 x^{\prime } = 4 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+2 x = \cos \left (\sqrt {2}\, t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x = \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+w^{2} x = \cos \left (\beta t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+3025 x = \cos \left (45 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime } = -\frac {x}{t^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime } = \frac {4 x}{t^{2}} \] |
✓ |
✓ |
|
|
\[ {}t^{2} x^{\prime \prime }+3 t x^{\prime }+x = 0 \] |
✓ |
✓ |
|
|
\[ {}t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t} = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} x^{\prime \prime }-7 t x^{\prime }+16 x = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} x^{\prime \prime }+3 t x^{\prime }-8 x = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} x^{\prime \prime }+t x^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} x^{\prime \prime }-t x^{\prime }+2 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+t^{2} x^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \tan \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-x = t \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-x = \frac {1}{t} \] |
✓ |
✓ |
|
|
\[ {}t^{2} x^{\prime \prime }-2 x = t^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \frac {1}{t +1} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-2 x^{\prime }+x = \frac {{\mathrm e}^{t}}{2 t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\frac {x^{\prime }}{t} = a \] |
✓ |
✓ |
|
|
\[ {}t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-x = \frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+t x^{\prime }+x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-t x^{\prime }+x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-2 a x^{\prime }+a^{2} x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-\frac {\left (2+t \right ) x^{\prime }}{t}+\frac {\left (2+t \right ) x}{t^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} x^{\prime \prime }+t x^{\prime }+\left (t^{2}-\frac {1}{4}\right ) x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime \prime }+x^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime \prime }+x^{\prime \prime } = 2 \,{\mathrm e}^{t}+3 t^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime \prime }+x^{\prime \prime }-x^{\prime }-4 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-x^{\prime }-6 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-2 x^{\prime }+2 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-2 x^{\prime }+2 x = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-x^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x = 1-\operatorname {Heaviside}\left (t -5\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+9 x = \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-2 x = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x = \cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\pi ^{2} x = \pi ^{2} \operatorname {Heaviside}\left (1-t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-4 x = 1-\operatorname {Heaviside}\left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+3 x^{\prime }+2 x = {\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-x = \delta \left (t -5\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \delta \left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right ) \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}x^{\prime \prime }+x = 3 \delta \left (t -2 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x = \frac {\left (t -5\right ) \operatorname {Heaviside}\left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = -8 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }-3 \left (1+x \right ) y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-x +1\right ) y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right ) y^{\prime \prime }-4 \left (1+x \right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{3}-x^{2}\right ) y^{\prime \prime }-\left (x^{3}+2 x^{2}-2 x \right ) y^{\prime }+\left (2 x^{2}+2 x -2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2-12 x +6 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-12 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }-14 y^{\prime }-5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime }+4 y^{\prime \prime }-7 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+15 y^{\prime \prime }+20 y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }+4 y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 y^{\prime \prime }-6 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+29 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+58 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 y^{\prime \prime }+6 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+37 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+9 y^{\prime }-5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+6 y^{\prime \prime }+2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }+13 y^{\prime }+30 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+8 y = 4 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 6 \sin \left (2 x \right )+7 \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 10 \sin \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+4 y = \cos \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-4 y = 16 x -12 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+5 y = 2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 5 \,{\mathrm e}^{-2 x} x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }+y^{\prime }-6 y = -18 x^{2}+1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-3 y^{\prime }-10 y = 8 \,{\mathrm e}^{-2 x} x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }+3 y^{\prime }-5 y = 5 \sin \left (2 x \right )+10 x^{2}+3 x +7 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+3 y = 3 x^{3}-8 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 6 \,{\mathrm e}^{-2 x}+3 \,{\mathrm e}^{x}-4 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 4 \,{\mathrm e}^{x}-18 \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 9 \,{\mathrm e}^{2 x}-8 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime } = 3 \,{\mathrm e}^{-x}+6 \,{\mathrm e}^{2 x}-6 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = x \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 3 x^{2} {\mathrm e}^{x}-7 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 12 x^{2}-16 x \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime } = 18 x^{2}+16 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x}-9 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+7 y^{\prime \prime }-5 y^{\prime }+6 y = 5 \sin \left (x \right )-12 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 16 x +20 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 9 \,{\mathrm e}^{2 x} x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 4 x \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = 8 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 27 \,{\mathrm e}^{-6 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 18 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+29 y = 8 \,{\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 8 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \,{\mathrm e}^{2 x} x +6 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 3 x^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 3 x^{2}-4 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 8 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y = 3 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-\sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }-4 y = 8 x^{2}+3-6 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = x^{3}+x +{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x}+{\mathrm e}^{3 x} \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-2 x} \left (\cos \left (x \right )+1\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = x^{4} {\mathrm e}^{x}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = x \,{\mathrm e}^{-3 x} \sin \left (2 x \right )+x^{2} {\mathrm e}^{-2 x} \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = x^{2} {\mathrm e}^{x}+3 \,{\mathrm e}^{2 x} x +5 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = {\mathrm e}^{2 x} x +x^{2} {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-x} x^{2}+3 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = x^{2} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = \cos \left (x \right )^{2}-\cosh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = \sin \left (2 x \right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cot \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right )^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sec \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-2 x} \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x} \tan \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 x}}{x^{3}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x} \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right )^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{x}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{{\mathrm e}^{2 x}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )+1} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \arcsin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \frac {{\mathrm e}^{-x}}{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+y = x \ln \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-6 x y^{\prime }+10 y = 3 x^{4}+6 x^{3} \] |
✓ |
✓ |
|
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\[ {}\left (1+x \right )^{2} y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = 1 \] |
✓ |
✓ |
|
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\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = \left (2+x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}x \left (-2+x \right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (-1+x \right ) y = 3 x^{2} \left (-2+x \right )^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right ) \left (1+x \right ) y^{\prime \prime }+2 x y^{\prime }-2 y = \left (2 x +1\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = x^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
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\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-6 x y^{\prime }+18 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 4 x -6 \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 2 x \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 4 \sin \left (\ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 y = 4 x -8 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = -6 x^{3}+4 x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 10 x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-6 y = \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (2+x \right )^{2} y^{\prime \prime }-\left (2+x \right ) y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+\left (3 x +2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+\left (-2+3 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-\left (-2+3 x \right ) y^{\prime }+2 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x +3\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}-3\right ) y^{\prime \prime }-2 x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x y^{\prime \prime }-\left (-2+x \right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (x^{2}+2\right ) y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}-x \right ) y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+\left (-2 x^{2}+3 x -2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+\frac {3 y}{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-3 x^{\prime }+2 x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}z^{\prime \prime }-4 z^{\prime }+13 z = 0 \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}\theta ^{\prime \prime }+4 \theta = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 z^{\prime \prime }+7 z^{\prime }-4 z = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+6 x^{\prime }+10 x = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{\prime \prime }-20 x^{\prime }+21 x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\omega ^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-4 x = t^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-4 x^{\prime } = t^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }-2 x = 3 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }-2 x = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+2 x^{\prime }+x = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\omega ^{2} x = \sin \left (\alpha t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\omega ^{2} x = \sin \left (\omega t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+6 x^{\prime }+10 x = {\mathrm e}^{-2 t} \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = {\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }-2 x = 12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x = 289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\omega ^{2} x = \cos \left (\alpha t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\omega ^{2} x = \cos \left (\omega t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime \prime \prime }-4 x^{\prime \prime \prime }+8 x^{\prime \prime }-8 x^{\prime }+4 x = \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime \prime \prime }-5 x^{\prime \prime }+4 x = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-\left (t^{2}+2 t \right ) y^{\prime }+\left (2+t \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-t^{2}+t \right ) x^{\prime \prime }+\left (-t^{2}+2\right ) x^{\prime }+\left (2-t \right ) x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-x = \frac {1}{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \cot \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}t^{2} x^{\prime \prime }-2 x = t^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-4 x^{\prime } = \tan \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} x^{\prime \prime }+t x^{\prime }-x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x = 0 \] |
✓ |
✓ |
|
|
\[ {}a y^{\prime \prime }+\left (-a +b \right ) y^{\prime }+c y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }-3 x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+10 y = 100 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \sin \left (t \right )-\cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime }+y^{\prime \prime \prime }-3 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )^{3}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cosh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-4 x^{\prime }+4 x = {\mathrm e}^{t}+{\mathrm e}^{2 t}+1 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime \prime \prime }-2 x^{\prime \prime }+x = t^{2}-3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 1-\frac {1}{\sin \left (x \right )} \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{r} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+9 x = t \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = \sinh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = x \,{\mathrm e}^{x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 y = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime \prime \prime }+2 x^{\prime \prime }+x = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 2 \cos \left (\ln \left (1+x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+10 x^{\prime }+25 x = 2^{t}+t \,{\mathrm e}^{-5 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\left (6\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime } = x +{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (3 x \right ) \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = y+x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-3 y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 x^{2} y^{\prime }+4 x y = 2 x \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 1-2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 2 x \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {2 x y^{\prime }}{2 x -1}-\frac {4 x y}{\left (2 x -1\right )^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime } = \left (25-6 x \right ) y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{1+x}-\frac {\left (2+x \right ) y}{x^{2} \left (1+x \right )} = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}\frac {\left (x^{2}-x \right ) y^{\prime \prime }}{x}+\frac {\left (1+3 x \right ) y^{\prime }}{x}+\frac {y}{x} = 3 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (5+2 x \right ) y^{\prime }+\left (4 x +8\right ) y = {\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-4 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-4 y^{\prime }+37 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-12 y^{\prime }+13 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-20 y^{\prime }+51 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+3 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
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\[ {}3 y^{\prime \prime }+8 y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
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\[ {}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \] |
✓ |
✓ |
|
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\[ {}4 y^{\prime \prime }+40 y^{\prime }+101 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+6 y^{\prime }+34 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+8 y^{\prime \prime }+16 y^{\prime } = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+13 y^{\prime } = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+13 y^{\prime } = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime } = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime } = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime } = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = 9 t \] |
✓ |
✓ |
|
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\[ {}4 y^{\prime \prime }+16 y^{\prime }+17 y = 17 t -1 \] |
✓ |
✓ |
|
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\[ {}4 y^{\prime \prime }+5 y^{\prime }+4 y = 3 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t^{2} {\mathrm e}^{2 t} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
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\[ {}2 y^{\prime \prime }-3 y^{\prime }+17 y = 17 t -1 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 2+t \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+8 y^{\prime }+20 y = \sin \left (2 t \right ) \] |
✓ |
✓ |
|
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\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = t^{2} \] |
✓ |
✓ |
|
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\[ {}2 y^{\prime \prime }+y^{\prime }-y = 4 \sin \left (t \right ) \] |
✓ |
✓ |
|
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\[ {}3 y^{\prime \prime }+5 y^{\prime }-2 y = 7 \,{\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+9 y = 24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime }+y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-1+t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-1+t \right )\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 39 \operatorname {Heaviside}\left (t \right )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (t -4\right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (t -4\right ) \] |
✓ |
✓ |
|
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\[ {}4 y^{\prime \prime }+4 y^{\prime }+5 y = 25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-1+t \right )+\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right . \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 \pi ^{2} y = 3 \delta \left (t -\frac {1}{3}\right )-\delta \left (-1+t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 3 \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y^{\prime }+29 y = 5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 1-\delta \left (-1+t \right ) \] |
✓ |
✓ |
|
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\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y = 8 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 4 t \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y = -t^{2}+2 t -10 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = t^{7} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 1 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-7 y = 4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 5 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }+5 y^{\prime }-2 y = 3 t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime } = 2 y^{\prime \prime }-4 y^{\prime }+\sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = x^{\frac {3}{2}} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 2 \sec \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = f \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x -\frac {1}{2}\right ) y^{\prime }+\frac {y}{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (1-5 x \right ) y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+4 y^{\prime }-x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
✗ |
✗ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+3 x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\alpha ^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\alpha ^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\beta y^{\prime }+\gamma y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 k y^{\prime }+k^{2} y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = a^{2} y \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = x^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 9 y \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+12 y = 7 y^{\prime } \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-a^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+9 y = 0 \] |
✓ |
✓ |
|
|
|
|||
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\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = x \] |
✓ |
✓ |
|
|
\[ {}s^{\prime \prime }-a^{2} s = t +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 8 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 5 x +2 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+5 y = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 6 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 2-6 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+3 y = {\mathrm e}^{-x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 2 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 2 x +3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 8 \cos \left (x a \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 h y^{\prime }+n^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+n^{2} y = h \sin \left (r x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \frac {1}{\cos \left (2 x \right )^{\frac {3}{2}}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = {\mathrm e}^{2 x} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-7 y^{\prime \prime }+12 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
✗ |
✗ |
|
|
\[ {}3 y^{\prime \prime }-2 y^{\prime }+4 y = x \] |
✓ |
✓ |
|
|
\[ {}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2} \] |
✓ |
✓ |
|
|
\[ {}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 31 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 27 x +18 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = -3 x -\frac {3}{x} \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+6 y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+35 y^{\prime \prime }+16 y^{\prime }-52 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\alpha y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+\left (-3-4 i\right ) y^{\prime \prime }+\left (-4+12 i\right ) y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+\left (-3-i\right ) y^{\prime \prime \prime }+\left (4+3 i\right ) y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 2 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 24 x^{2}-6 x +14+32 \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3+\cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = 6 x -20-120 x^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y = 36 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = \left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y = {\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 2 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 x +4 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-9 y = 2 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{x}-3 x^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x \,{\mathrm e}^{x}-3 x^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-9 y = 2+x \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+9 y = 2+x \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }+6 y = -2 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = -x^{2}+1 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x +\cos \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+9 y = 1 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+9 y = 18 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-2 y = x^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (-1+x \right )^{2} & 1\le x \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \delta \left (x -\pi \right )+\delta \left (x -3 \pi \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \delta \left (-1+x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = \cos \left (x \right )+2 \delta \left (x -\pi \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y = \cos \left (x \right ) \delta \left (x -\pi \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+a^{2} y = \delta \left (x -\pi \right ) f \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-6 y^{\prime }-7 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \,{\mathrm e}^{-3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 4 \,{\mathrm e}^{-3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 3 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-\frac {t}{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-\frac {t}{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 5 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 10 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+6 y = -8 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y = -3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 6 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y = -{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = -3 t^{2}+2 t +3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 3 t +2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 3 t +2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = t -\frac {1}{20} t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 4+{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-t}-4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = t +{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 6+t^{2}+{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 5 \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 2 \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = -4 \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 3 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = -\cos \left (5 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+y = \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 3+2 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-t} \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 5 \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = -\cos \left (\frac {t}{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 3 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 2 \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 8 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = {\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 2 \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (t -4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y = 5 \delta \left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = -2 \delta \left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (-1+t \right )-3 \delta \left (t -4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = {\mathrm e}^{-2 t} \sin \left (4 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {1+x}{-1+x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+8 y = {\mathrm e}^{-x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 = x \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 = \sqrt {x} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime } = 2 y^{\prime } \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = y^{\prime } \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}x y^{\prime \prime } = y^{\prime }-2 x^{2} y^{\prime } \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 2 y^{\prime }-6 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime } = y^{\prime \prime } \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime } x +2 y^{\prime \prime } = 6 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime } = 2 \sqrt {y^{\prime \prime }} \] |
✗ |
✓ |
|
|
\[ {}y^{\prime \prime } = y^{\prime } \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = 6 x^{5} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime } = 2 y^{\prime } \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = y^{\prime } \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime } = y^{\prime \prime } \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime } x +2 y^{\prime \prime } = 6 x \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime } = 6 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }-83 y-25 = 0 \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime } = y \] |
✗ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\left (4+\frac {2}{x}\right ) y^{\prime }+\left (4+\frac {4}{x}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}-4 x^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = \sqrt {x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-20 y = 27 x^{5} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1+x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y = {\mathrm e}^{3 x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y = 0 \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
✗ |
✗ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0 \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-10 y^{\prime \prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-24 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }+7 y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}25 y^{\prime \prime }-10 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}16 y^{\prime \prime }-24 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 y^{\prime \prime }+12 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+29 y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 y^{\prime \prime }+18 y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+\left (\frac {1}{4}+4 \pi ^{2}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+\left (\frac {1}{4}+4 \pi ^{2}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-34 y^{\prime \prime }+225 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-8 y^{\prime \prime }+37 y^{\prime }-50 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-9 y^{\prime \prime }+31 y^{\prime }-39 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+2 y^{\prime \prime }+4 y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+10 y^{\prime \prime }+18 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+26 y^{\prime \prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+9 y^{\prime \prime }+9 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime \prime }+15 y^{\prime \prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-19 x y^{\prime }+100 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+29 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+29 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+37 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-11 x y^{\prime }+36 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 x y^{\prime }-18 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 x y^{\prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 x y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 24 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 24 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-8 y = 8 x^{2}-3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-8 y = 8 x^{2}-3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = 36 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -6 \,{\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 7 \,{\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 169 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 10 x +12 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = {\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = {\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 35 \,{\mathrm e}^{5 x}+12 \,{\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 22 x +24 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = x \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 4 x^{2}+2 x +3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 52 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = 30 \,{\mathrm e}^{-4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{\frac {x}{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -5 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 10 \cos \left (2 x \right )+15 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 25 \sin \left (6 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -4 \cos \left (x \right )+7 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -200 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 18 x^{2}+3 x +4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 9 x^{4}-9 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 54 x^{2} {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 6 x \,{\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left (12 x -4\right ) {\mathrm e}^{-5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 39 \,{\mathrm e}^{2 x} x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -3 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 20 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 3 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 10 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = \left (72 x^{2}-1\right ) {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 4 x \,{\mathrm e}^{6 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{-5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 24 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 8 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{-x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 100 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 10 x^{2}+4 x +8 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 6 \cos \left (x \right )-3 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 6 \cos \left (2 x \right )-3 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{-x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{2 x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{-8 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{4 x} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{2 x} \sin \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = x^{3} \sin \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{2} {\mathrm e}^{5 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{4} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = x^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 \cos \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 6 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 x \cos \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 3 x \cos \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 3 x \,{\mathrm e}^{x} \cos \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 5 x^{5} {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right )+3 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 5 \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 20 \sinh \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = \frac {5}{x^{3}} \] |
✓ |
✓ |
|
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\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {50}{x^{3}} \] |
✓ |
✓ |
|
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\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 85 \cos \left (2 \ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 y = 15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y = 4 x^{3} \] |
✓ |
✓ |
|
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\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = \frac {10}{x} \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 6 x^{3} \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 64 \ln \left (x \right ) x^{2} \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 3 \sqrt {x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = \cot \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y = \csc \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 6 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \left (24 x^{2}+2\right ) {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}+1} \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = \sqrt {x} \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 12 x^{3} \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{2} \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \ln \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-2 y = \frac {1}{-2+x} \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = x^{3} {\mathrm e}^{x^{2}} \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1+x \right )^{2} \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = \frac {10}{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 12 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = {\mathrm e}^{-x^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 x y^{\prime }+9 y = 12 x \sin \left (x^{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+36 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-36 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y^{\prime }+14 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+y^{\prime } = \sqrt {x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\frac {5 y}{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-30 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-30 y = 0 \] |
✓ |
✓ |
|
|
\[ {}16 y^{\prime \prime }-8 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime } = 8 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-7 y^{\prime }+3 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+20 y^{\prime }+100 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime } = 3 y^{\prime } \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y^{\prime }+14 y = 98 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 25 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y^{\prime }+14 y = 576 \,{\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 81 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 3 \sqrt {x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+36 y = 6 \sec \left (6 x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 18 \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }-2 y = 10 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 2 \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 6 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = \frac {1}{x^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = x \,{\mathrm e}^{\frac {3 x}{2}} \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }+8 y^{\prime }-3 y = 123 x \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1+x \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = t^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 20 \,{\mathrm e}^{4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = t^{2} {\mathrm e}^{4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 7 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }+y^{\prime }+t y = 0 \] |
✗ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 27 t^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+7 y = 165 \,{\mathrm e}^{4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t^{2} {\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+17 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = {\mathrm e}^{t} \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+40 y = 122 \,{\mathrm e}^{-3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = 24 \,{\mathrm e}^{-3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = {\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -10\right ) \] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1 |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1 |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \delta \left (t -3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \delta \left (-1+t \right )-\delta \left (t -4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t \right )+\delta \left (t -\pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = -2 \delta \left (t -\frac {\pi }{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = \delta \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = \delta \left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-16 y = \delta \left (t -10\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t \right ) \] |
✓ |
✗ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right ) \] |
✓ |
✗ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (t -4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right ) \] |
✓ |
✗ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }-5 x y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-2 x +2\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-2 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\lambda y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (6 x^{2}+2 x +1\right ) y^{\prime }+\left (2+12 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x -3\right )^{2} y^{\prime \prime }-2 \left (x -3\right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }-5 \left (-1+x \right ) y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2+x \right )^{2} y^{\prime \prime }+\left (2+x \right ) y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}3 \left (-2+x \right )^{2} y^{\prime \prime }-4 \left (x -5\right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x -5\right )^{2} y^{\prime \prime }+\left (x -5\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+4\right )^{2} y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 x y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+\frac {y}{1-x} = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+\left (-2 x^{3}+5 x \right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-3 x^{3}+3 x^{2}\right ) y^{\prime \prime }-\left (5 x^{2}+4 x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 x y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (-x^{4}+x \right ) y^{\prime }+3 x^{3} y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{2+x}+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x -3\right )^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (-x^{2}+2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (2+x \right )^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (2+x \right )^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0 \] |
✓ |
✓ |
|
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\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 x y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y^{\prime }-2 y = x^{3} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+5 y^{\prime }+y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+2 x^{\prime }-10 x = 0 \] |
✓ |
✓ |
|
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\[ {}x^{\prime \prime }+x = t \cos \left (t \right )-\cos \left (t \right ) \] |
✓ |
✓ |
|
|
|
|||
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\[ {}y^{\prime \prime }-12 y^{\prime }+40 y = 0 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-12 x y^{\prime }+42 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-12 t y^{\prime }+42 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}16 y^{\prime \prime }+24 y^{\prime }+153 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+\frac {25 y^{\prime \prime }}{2}-5 y^{\prime }+\frac {629 y}{16} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+45 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = 2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = t \] |
✗ |
✗ |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}} = \frac {1}{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 t^{2} y^{\prime \prime }-3 t y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 t^{2} y^{\prime \prime }-5 t y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }-7 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+10 y^{\prime }+24 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+18 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+10 y^{\prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+49 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+4 t y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+6 t y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}a y^{\prime \prime }+b y^{\prime }+c y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+a t y^{\prime }+b y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (36 t^{2}-1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }+2 y^{\prime }+16 t y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }-12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}8 y^{\prime \prime }+6 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+21 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}7 y^{\prime \prime }+4 y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }-y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-7 y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+36 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+100 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 y^{\prime \prime }+5 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 y^{\prime \prime }+6 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}a y^{\prime \prime }+2 b y^{\prime }+c y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }-16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 8 \,{\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = -{\mathrm e}^{-9 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 2 \,{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 2 t -4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 3-4 t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 4 \cos \left (t \right )-\sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \cos \left (2 t \right )+t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 3 t \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 3 t^{4}-2 t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = -1 \] |
✓ |
✓ |
|
|
\[ {}5 y^{\prime \prime }+y^{\prime }-4 y = -3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 32 t \] |
✓ |
✓ |
|
|
\[ {}16 y^{\prime \prime }-8 y^{\prime }-15 y = 75 t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+26 y = -338 t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = -32 t^{2} \] |
✓ |
✓ |
|
|
\[ {}8 y^{\prime \prime }+6 y^{\prime }+y = 5 t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = -256 t^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 52 \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 25 \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = 54 t \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = -78 \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = -32 t^{2} \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-20 y = -2 \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }-5 y = -648 t^{2} {\mathrm e}^{5 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = -2 t^{3} {\mathrm e}^{4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = t^{2}+{\mathrm e}^{t}+\sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 18 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 32 t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = -2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 3 t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = 4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = t \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = -1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = -{\mathrm e}^{3 t}-2 t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = -3 t -4 t^{2} {\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 2 t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = {\mathrm e}^{-3 t}-{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 \pi ^{2} y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 2 t -2 \pi & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 10 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = f \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+9 x = \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+37 y = \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y^{\prime } = t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = {\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 2 \cos \left (4 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 2 t \,{\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y}{4} = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = \csc \left (4 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = \cot \left (4 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+50 y = {\mathrm e}^{-t} \csc \left (7 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = {\mathrm e}^{-3 t} \left (\sec \left (4 t \right )+\csc \left (4 t \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+26 y = {\mathrm e}^{t} \left (\sec \left (5 t \right )+\csc \left (5 t \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+12 y^{\prime }+37 y = {\mathrm e}^{-6 t} \csc \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+34 y = {\mathrm e}^{3 t} \tan \left (5 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+34 y = {\mathrm e}^{5 t} \cot \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-12 y^{\prime }+37 y = {\mathrm e}^{6 t} \sec \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 t} \sec \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-25 y = \frac {1}{1-{\mathrm e}^{5 t}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 2 \sinh \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 t}}{t^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{4}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 t}}{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \ln \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{t}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{-2 t} \sqrt {-t^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \sqrt {-t^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 t} \ln \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 t} \arctan \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \tan \left (3 t \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sec \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \tan \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \tan \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = \tan \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \tan \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sec \left (3 t \right ) \tan \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sec \left (2 t \right ) \tan \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \frac {\csc \left (3 t \right )}{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sec \left (2 t \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-16 y = 16 t \,{\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (t \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sec \left (2 t \right )+\tan \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \csc \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 65 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = \ln \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+4 y = t \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 2 \ln \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = f \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y = t^{3}+2 t \] |
✗ |
✗ |
|
|
\[ {}t y^{\prime \prime }+2 y^{\prime }+t y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }+2 y^{\prime }+t y = -t \] |
✓ |
✓ |
|
|
\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{\frac {3}{2}} \] |
✗ |
✗ |
|
|
|
|||
|
\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{\frac {3}{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-10 y^{\prime \prime }+25 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}8 y^{\prime \prime \prime }+y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+16 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-9 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }-y^{\prime \prime }+54 y^{\prime }-72 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+7 y^{\prime \prime \prime }+6 y^{\prime \prime }-32 y^{\prime }-32 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (6\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (6\right )}+12 y^{\prime \prime \prime \prime }+48 y^{\prime \prime }+64 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}24 y^{\prime \prime \prime }-26 y^{\prime \prime }+9 y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}8 y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+66 y^{\prime \prime \prime }-41 y^{\prime \prime }-37 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\left (5\right )}+7 y^{\prime \prime \prime \prime }+17 y^{\prime \prime \prime }+17 y^{\prime \prime }+5 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+9 y^{\prime \prime }+16 y^{\prime }-26 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+60 y^{\prime \prime }+124 y^{\prime }+75 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+30 y^{\prime \prime }-56 y^{\prime }+49 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\frac {31 y^{\prime \prime \prime }}{100}+\frac {56 y^{\prime \prime }}{5}-\frac {49 y^{\prime }}{5}+\frac {53 y}{10} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+9 y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+9 y^{\prime \prime } = 9 \,{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+10 y^{\prime \prime }+34 y^{\prime }+40 y = t \,{\mathrm e}^{-4 t}+2 \,{\mathrm e}^{-3 t} \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \,{\mathrm e}^{-3 t}-t \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-24 y^{\prime }+36 y = 108 t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }-14 y^{\prime }-104 y = -111 \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-10 y^{\prime \prime \prime }+38 y^{\prime \prime }-64 y^{\prime }+40 y = 153 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = \sec \left (2 t \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = \tan \left (2 t \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime } = -\frac {1}{t^{2}}-\frac {2}{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = \frac {{\mathrm e}^{t}}{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }-11 y^{\prime }+30 y = {\mathrm e}^{4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-10 y^{\prime }-24 y = {\mathrm e}^{-3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime } = \tan \left (t \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime } = 3 t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime } = \sec \left (t \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime } = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime } = t \] |
✓ |
✓ |
|
|
\[ {}t^{2} \ln \left (t \right ) y^{\prime \prime \prime }-t y^{\prime \prime }+y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}\left (t^{2}+t \right ) y^{\prime \prime \prime }+\left (-t^{2}+2\right ) y^{\prime \prime }-\left (2+t \right ) y^{\prime } = -t -2 \] |
✓ |
✓ |
|
|
\[ {}2 t^{3} y^{\prime \prime \prime }+t^{2} y^{\prime \prime }+t y^{\prime }-y = -3 t^{2} \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-8 x y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-7 x y^{\prime }+7 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+17 y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }-9 x y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-2 x y^{\prime }+20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+22 x^{2} y^{\prime \prime }+124 x y^{\prime }+140 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }-46 x y^{\prime }+100 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+7 x y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \frac {1}{x^{5}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = \frac {1}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = \frac {1}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 2 x \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 8 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+36 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-11 x y^{\prime }+16 y = \frac {1}{x^{3}} \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+70 x y^{\prime }+80 y = \frac {1}{x^{13}} \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-7 x y^{\prime }+7 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+10 x^{2} y^{\prime \prime }-20 x y^{\prime }+20 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+54 x y^{\prime }+42 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+5 x y^{\prime }-5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+17 x y^{\prime }-17 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+27 x y^{\prime }+10 y = \frac {1}{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 x y^{\prime } = -8 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (4 x^{2}-4\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 x y^{\prime }+125 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-12 x^{2} y^{\prime \prime }-12 x y^{\prime }+48 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+14 x^{3} y^{\prime \prime \prime }+55 x^{2} y^{\prime \prime }+65 x y^{\prime }+15 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+35 x y^{\prime }+45 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+10 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+21 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 x y^{\prime }+58 y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 x^{2} y^{\prime \prime }+5 x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+7 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-18 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-11 y^{\prime }+30 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}\left (3 x +2\right ) y^{\prime \prime }+3 x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+2\right ) y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+2\right ) y^{\prime \prime }+2 x y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime } = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+9 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }-5 y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }-7 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (t +1\right )^{2} y^{\prime \prime }-2 \left (t +1\right ) y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }+2 y^{\prime }+t y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}6 y^{\prime \prime }+5 y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+34 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-5 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}15 y^{\prime \prime }-11 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}20 y^{\prime \prime }+y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}12 y^{\prime \prime }+8 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}9 y^{\prime \prime \prime }+36 y^{\prime \prime }+40 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}9 y^{\prime \prime \prime }+12 y^{\prime \prime }+13 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = -t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime } = 5 t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = -3 \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = \frac {1}{{\mathrm e}^{2 t}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = -4 \,{\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 3 \,{\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y^{\prime }+20 y = -2 t \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 3 t^{2} {\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }+5 y = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+18 y^{\prime \prime }+30 y^{\prime }+25 y = {\mathrm e}^{-t} \cos \left (2 t \right )+{\mathrm e}^{-2 t} \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }+20 y^{\prime }+25 y = t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+10 y^{\prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \tan \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \csc \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \ln \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \ln \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 t y^{\prime }+t^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}5 x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+25 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 8 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }-10 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{\prime \prime }+9 x = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x^{\prime \prime }+4 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+64 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+100 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+16 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+256 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+9 x = 0 \] |
✓ |
✓ |
|
|
\[ {}10 x^{\prime \prime }+\frac {x}{10} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+3 x = 0 \] |
✓ |
✓ |
|
|
\[ {}\frac {x^{\prime \prime }}{32}+2 x^{\prime }+x = 0 \] |
✓ |
✓ |
|
|
\[ {}\frac {x^{\prime \prime }}{4}+2 x^{\prime }+x = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{\prime \prime }+2 x^{\prime }+8 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+13 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+20 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+13 x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 1-t & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \cos \left (\frac {9 t}{10}\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \cos \left (\frac {7 t}{10}\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\frac {x^{\prime }}{10}+x = 3 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-3 x^{\prime }+4 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+6 x^{\prime }+9 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+16 x = t \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \cos \left (x \right )+2 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } \left (2+x \right )^{5} = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 2 x \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime } = y^{\prime } \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime } = \left (2 x^{2}+1\right ) y^{\prime } \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime } = y^{\prime }+x^{2} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime \prime }-y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+2 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }-2 y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-8 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+10 y^{\prime \prime }+12 y^{\prime }+5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }-5 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime } = \left (-1+x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime } = {\mathrm e}^{-7 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \left (1-x \right ) {\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-3 y^{\prime } = x \,{\mathrm e}^{\frac {3 x}{4}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = x \,{\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+25 y = \cos \left (5 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right )-\cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = \sin \left (4 x +\alpha \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )+\cos \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )-\cos \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = {\mathrm e}^{-3 x} \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+k^{2} y = k \sin \left (k x +\alpha \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+k^{2} y = k \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime } = 3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime } = 3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = x \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = x \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y = a \sin \left (n x +\alpha \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 n^{2} y^{\prime \prime }+n^{4} y = \cos \left (n x +\alpha \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = -2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = -2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 9 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}5 y^{\prime \prime \prime }-7 y^{\prime \prime } = 3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime } = 8 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 k y^{\prime }+k^{2} y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 8 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 9 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}7 y^{\prime \prime }-y^{\prime } = 14 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 3 x \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 10 \left (1-x \right ) {\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 1+x \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y^{\prime }+y = \left (x^{2}+x \right ) {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-2 y = 8 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 4 x \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 m y^{\prime }+m^{2} y = \sin \left (n x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a^{2} y = 2 \cos \left (m x \right )+3 \sin \left (m x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 4 \left (\cos \left (x \right )+\sin \left (x \right )\right ) {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 10 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+8 y^{\prime } = x \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y^{\prime }-2 y = x^{2} {\mathrm e}^{4 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \left (x^{2}+x \right ) {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = x^{2}+x \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime } = x^{2}+x \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = x^{2} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x} \cos \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \left (\sin \left (x \right )+2 \cos \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{x}+{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = x +{\mathrm e}^{-4 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y = x +\sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = \left (\sin \left (x \right )+1\right ) {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime } = 1+{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 x \right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 2 \cos \left (4 x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 4 x -2 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 18 x -10 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2+{\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \left (5 x +4\right ) {\mathrm e}^{x}+{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-3 y^{\prime }-2 y = 5 \,{\mathrm e}^{x} \cosh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = x \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = x \,{\mathrm e}^{x}+\frac {\cos \left (x \right )}{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 10 \sin \left (x \right )+17 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x^{2}-{\mathrm e}^{-x}+{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 2 x +{\mathrm e}^{-x}-2 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = {\mathrm e}^{x}+4 \sin \left (2 x \right )+2 \cos \left (x \right )^{2}-1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 6 x \,{\mathrm e}^{-x} \left (1-{\mathrm e}^{-x}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cos \left (2 x \right )^{2}+\sin \left (\frac {x}{2}\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 1+8 \cos \left (x \right )+{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (\frac {x}{2}\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x} \left (1-2 \sin \left (x \right )^{2}\right )+10 x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 4 x +\sin \left (x \right )+\sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 1+2 \cos \left (x \right )+\cos \left (2 x \right )-\sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y+1 = \sin \left (x \right )+x +x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 18 \,{\mathrm e}^{-3 x}+8 \sin \left (x \right )+6 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+1 = 3 \sin \left (2 x \right )+\cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x}+2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \sin \left (2 x \right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime } = 4 x +3 \sin \left (x \right )+\cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2-2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 9 x^{2}-12 x +2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 36 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \left (12 x -7\right ) {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 4 x \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 2 x^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 16 \,{\mathrm e}^{-x}+9 x -6 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = -5 \,{\mathrm e}^{-x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 4 \,{\mathrm e}^{x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \cos \left (2 x \right )+\sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = -2 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-x} \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 8 \,{\mathrm e}^{x}+9 \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-5 y = 1 \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right ) \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right ) \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right ) \] |
✗ |
✗ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }+6 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2+x \right )^{2} y^{\prime \prime }+3 \left (2+x \right ) y^{\prime }-3 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-3 x y^{\prime \prime }+3 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = x \left (6-\ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 y = \sin \left (\ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = -\frac {16 \ln \left (x \right )}{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y = x^{2}-2 x +2 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 \ln \left (x \right )^{2}+12 x \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}\left (1+x \right )^{3} y^{\prime \prime }+3 \left (1+x \right )^{2} y^{\prime }+\left (1+x \right ) y = 6 \ln \left (1+x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (-2+x \right )^{2} y^{\prime \prime }-3 \left (-2+x \right ) y^{\prime }+4 y = x \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right ) y^{\prime \prime }+\left (-2+4 x \right ) y^{\prime }-8 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (1+x \right ) y^{\prime }+6 y = 6 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 5 x^{4} \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = \left (-1+x \right )^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{4}-x^{3}\right ) y^{\prime \prime }+\left (2 x^{3}-2 x^{2}-x \right ) y^{\prime }-y = \frac {\left (-1+x \right )^{2}}{x} \] |
✓ |
✓ |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y = x^{2} \left (2 x -3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \frac {1}{1+{\mathrm e}^{x}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \frac {1}{\cos \left (x \right )^{3}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \frac {{\mathrm e}^{-x}}{\sin \left (x \right )} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \frac {2}{\sin \left (x \right )^{3}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime } = \frac {-1+x}{x^{3}} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime } = 4 x^{3} {\mathrm e}^{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (2 x -1\right ) y^{\prime } = -4 x^{2} \] |
✓ |
✓ |
|
|
\[ {}4 x y^{\prime \prime }+2 y^{\prime }+y = 1 \] |
✗ |
✗ |
|
|
\[ {}4 x y^{\prime \prime }+2 y^{\prime }+y = \frac {6+x}{x^{2}} \] |
✗ |
✗ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {1}{x^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (-1+x \right )^{2} {\mathrm e}^{x} \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y = 4 \,{\mathrm e}^{x} \] |
✗ |
✗ |
|
|
\[ {}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-2 \left (1-x \right ) y = 2 x -2 \] |
✗ |
✗ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+2 x^{\prime }+6 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+2 x^{\prime }+x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\lambda y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\lambda y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✗ |
✗ |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\alpha y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\alpha ^{2} y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\lambda ^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\lambda ^{2} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0 \] |
✗ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-\lambda ^{4} y = 0 \] |
✗ |
✓ |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }+4 x y^{\prime \prime \prime }+2 y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\left (x^{2}+1\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \cos \left (x \right )^{2} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \pi ^{2}-x^{2} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-4 y = \cos \left (\pi x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \arcsin \left (\sin \left (x \right )\right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+9 y = \sin \left (x \right )^{3} \] |
✓ |
✓ |
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\[ {}x^{\prime \prime } = 0 \] |
✓ |
✓ |
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\[ {}x^{\prime \prime } = 1 \] |
✓ |
✓ |
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\[ {}x^{\prime \prime } = \cos \left (t \right ) \] |
✓ |
✓ |
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\[ {}x^{\prime \prime }+x^{\prime } = 0 \] |
✓ |
✓ |
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\[ {}x^{\prime \prime }+x^{\prime } = 0 \] |
✓ |
✓ |
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\[ {}x^{\prime \prime }-x^{\prime } = 1 \] |
✓ |
✓ |
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\[ {}x^{\prime \prime }+x = t \] |
✓ |
✓ |
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\[ {}x^{\prime \prime }+6 x^{\prime } = 12 t +2 \] |
✓ |
✓ |
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\[ {}x^{\prime \prime }-2 x^{\prime }+2 x = 2 \] |
✓ |
✓ |
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\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 4 \] |
✓ |
✓ |
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\[ {}2 x^{\prime \prime }-2 x^{\prime } = \left (t +1\right ) {\mathrm e}^{t} \] |
✓ |
✓ |
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\[ {}x^{\prime \prime }+x = 2 \cos \left (t \right ) \] |
✓ |
✓ |
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