This table gives the list of problem which are second order or higher and inhomogeneous (i.e. the RHS of the ode is not zero).
Number of problems in this table is 2730
|
# |
ODE |
Solved? |
Verified? |
|
\[ {}y^{\prime \prime }+y = 3 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 12 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 6 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y = 4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y = 6 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y = 6 x +4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 3 x +4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 2 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 3 x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+4 y^{\prime }+7 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = \sinh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = \cosh \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 1+x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 2 \cos \left (3 x \right )+3 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 2 x^{2} {\mathrm e}^{3 x}+5 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 3 x \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = x \left (-{\mathrm e}^{-2 x}+{\mathrm e}^{-x}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = x \,{\mathrm e}^{3 x} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 1+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sin \left (x \right )^{4} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x \cos \left (x \right )^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 4 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 3 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = \sinh \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \cos \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 2 \sec \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \csc \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{4} \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 8 x^{\frac {4}{3}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}-1 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+9 x = 10 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x = 5 \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+100 x = 225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+25 x = 90 \cos \left (4 t \right ) \] |
✓ |
✓ |
|
|
\[ {}m x^{\prime \prime }+k x = F_{0} \cos \left (\omega t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 10 \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+3 x^{\prime }+5 x = -4 \cos \left (5 t \right ) \] |
✓ |
✓ |
|
|
\[ {}2 x^{\prime \prime }+2 x^{\prime }+x = 3 \sin \left (10 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+3 x^{\prime }+3 x = 8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+5 x = 10 \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+2 x^{\prime }+26 x = 600 \cos \left (10 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+8 x^{\prime }+25 x = 200 \cos \left (t \right )+520 \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 2 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 16 \,{\mathrm e}^{\frac {t}{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 9 \sec \left (3 t \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 t}}{t^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 3 \csc \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \sec \left (\frac {t}{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = g \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = g \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1 \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-t \left (2+t \right ) y^{\prime }+\left (2+t \right ) y = 2 t^{3} \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = t^{2} {\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (-1+t \right )^{2} {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \ln \left (x \right ) x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = g \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 4 t^{2} \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = t^{2} {\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (-1+t \right ) {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (\frac {t}{4}\right ) \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (6 t \right ) \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5} = \cos \left (t \right ) \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y = t \] |
✓ |
✓ |
|
|
\[ {}t \left (-1+t \right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y = 0 \] |
✗ |
N/A |
|
|
\[ {}t^{2} \left (3+t \right ) y^{\prime \prime \prime }-3 t \left (2+t \right ) y^{\prime \prime }+6 \left (t +1\right ) y^{\prime }-6 y = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\omega ^{2} y = \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t <\infty \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & \pi \le t <2 \pi \\ 0 & \operatorname {otherwise} \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \operatorname {otherwise} \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 1-\operatorname {Heaviside}\left (t -\pi \right ) \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right ) \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2} \] |
✓ |
✓ |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )-\operatorname {Heaviside}\left (t -5-k \right ) \left (t -5-k \right )}{k} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = \sin \left (t \right )+\delta \left (t -3 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 2 \delta \left (t -\frac {\pi }{4}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{2}+y = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{4}+y = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \frac {\operatorname {Heaviside}\left (t -4+k \right )-\operatorname {Heaviside}\left (t -4-k \right )}{2 k} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = f \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = \left (2 x +1\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = \frac {4}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 7 x^{\frac {3}{2}} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x} \left (1+4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 8 \,{\mathrm e}^{-x \left (2+x \right )} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = -6 x -4 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x \left (-1+x \right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y = x^{3} {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y = x^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}\left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y = \left (4 x^{2}-4 x +1\right ) {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 4 x^{4} \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+\left (1+4 x \right ) y^{\prime }+\left (2 x +1\right ) y = 3 \sqrt {x}\, {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = -{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y = 4 x^{\frac {5}{2}} {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 4 x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 4 x^{4} \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y = \left (1+x \right )^{3} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-4\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 2+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \tan \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 x \right ) \sec \left (2 x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {4}{1+{\mathrm e}^{-x}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 3 \,{\mathrm e}^{x} \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 14 x^{\frac {3}{2}} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \frac {4 \,{\mathrm e}^{-x}}{1-{\mathrm e}^{-2 x}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 2 x^{2}+2 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (-2+x \right ) y = {\mathrm e}^{2 x} \] |
✗ |
N/A |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 4 \,{\mathrm e}^{-x \left (2+x \right )} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{\frac {5}{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 2 x^{4} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y = \left (2 x +1\right )^{2} {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+2 y^{\prime }+2 y = \sin \left (\sqrt {x}\right ) \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y = 6 x^{3} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y = x^{1+a} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = x^{3} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{5} \] |
✓ |
✓ |
|
|
\[ {}\sin \left (x \right ) y^{\prime \prime }+\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime }+\left (\sin \left (x \right )-\cos \left (x \right )\right ) y = {\mathrm e}^{-x} \] |
✗ |
N/A |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 8 x^{\frac {5}{2}} \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}+3\right ) y = x^{\frac {7}{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y = 3 x^{4} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = x^{3} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = x^{\frac {3}{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+2 \left (x +3\right ) y = x^{4} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (2+x \right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y = 2 x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = x^{4} \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 2 \left (-1+x \right )^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y = x^{\frac {5}{2}} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = \left (3 x -1\right )^{2} {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }+2 y = \left (-1+x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+\left (-1+x \right )^{3} y = \left (-1+x \right )^{3} {\mathrm e}^{x} \] |
✗ |
N/A |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 x \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = -2 x^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right ) \left (2 x +3\right ) y^{\prime \prime }+2 \left (2+x \right ) y^{\prime }-2 y = \left (2 x +3\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = -{\mathrm e}^{x} \left (-24 x^{2}+76 x +4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{-3 x} \left (6 x^{2}-23 x +32\right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y = -{\mathrm e}^{x} \left (6 x^{2}+45 x +4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y = {\mathrm e}^{-2 x} \left (3 x^{2}-17 x +2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y = {\mathrm e}^{x} \left (16 x^{3}+24 x^{2}+2 x -1\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-2 y = {\mathrm e}^{x} \left (15 x^{2}+34 x +14\right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y = -{\mathrm e}^{-2 x} \left (1-15 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = -{\mathrm e}^{x} \left (7+6 x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime }-7 y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{2 x} \left (17+30 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+3 y^{\prime }+9 y = 2 \,{\mathrm e}^{3 x} \left (11-24 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-7 y^{\prime \prime }+8 y^{\prime }+16 y = 2 \,{\mathrm e}^{4 x} \left (13+15 x \right ) \] |
✓ |
✓ |
|
|
\[ {}8 y^{\prime \prime \prime }-12 y^{\prime \prime }+6 y^{\prime }-y = {\mathrm e}^{\frac {x}{2}} \left (1+4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }-7 y^{\prime }+6 y = -3 \,{\mathrm e}^{-x} \left (-8 x^{2}+8 x +12\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-2 y = -3 \,{\mathrm e}^{2 x} \left (11+12 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime } = -16 \,{\mathrm e}^{-2 x} \left (-x^{3}+x^{2}+x +1\right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime \prime }-11 y^{\prime \prime }-9 y^{\prime }-2 y = -{\mathrm e}^{x} \left (1-6 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \left (x^{2}+4 x +3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+2 y = {\mathrm e}^{2 x} \left (x^{4}+x +24\right ) \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-5 y^{\prime }-2 y = 18 \,{\mathrm e}^{x} \left (5+2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }-4 y = -{\mathrm e}^{2 x} \left (15 x^{2}+28 x +4\right ) \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime }-y = 3 \,{\mathrm e}^{-\frac {x}{2}} \left (1-6 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = {\mathrm e}^{x} \left (-3 x^{2}+x +3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{2 x} \left (18 x^{2}+33 x +13\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime } = {\mathrm e}^{2 x} \left (12 x^{2}+26 x +15\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y = {\mathrm e}^{x} \left (1+x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-y = {\mathrm e}^{x} \left (11+12 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x} \left (10 x^{2}-24 x +5\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (-5 x^{2}-8 x +3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (\left (16+10 x \right ) \cos \left (x \right )+\left (30-10 x \right ) \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y = {\mathrm e}^{-x} \left (\left (1-22 x \right ) \cos \left (2 x \right )-\left (6 x +1\right ) \sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }-2 y = {\mathrm e}^{2 x} \left (\left (-x^{2}+5 x +27\right ) \cos \left (x \right )+\left (9 x^{2}+13 x +2\right ) \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y = -{\mathrm e}^{x} \left (\left (4 x^{2}+5 x +9\right ) \cos \left (2 x \right )-\left (-3 x^{2}-5 x +6\right ) \sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }+12 y = 8 \cos \left (2 x \right )-16 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+2 y = {\mathrm e}^{x} \left (\left (20+4 x \right ) \cos \left (x \right )-\left (12+12 x \right ) \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-7 y^{\prime \prime }+20 y^{\prime }-24 y = -{\mathrm e}^{2 x} \left (\left (13-8 x \right ) \cos \left (2 x \right )-\left (-4 x +8\right ) \sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+18 y^{\prime } = -{\mathrm e}^{3 x} \left (\left (2-3 x \right ) \cos \left (3 x \right )-\left (3+3 x \right ) \sin \left (3 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-8 y^{\prime }-8 y = {\mathrm e}^{x} \left (8 \cos \left (x \right )+16 \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }-4 y = {\mathrm e}^{x} \left (2 \cos \left (2 x \right )-\sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+15 y = {\mathrm e}^{2 x} \left (15 x \cos \left (2 x \right )+32 \sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+13 y^{\prime \prime }+12 y^{\prime }+4 y = {\mathrm e}^{-x} \left (\left (4-x \right ) \cos \left (x \right )-\left (5+x \right ) \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }-4 y = -{\mathrm e}^{-x} \left (-\sin \left (x \right )+\cos \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y = {\mathrm e}^{x} \left (\sin \left (2 x \right )+\cos \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+32 y^{\prime \prime }+64 y^{\prime }+39 y = {\mathrm e}^{-2 x} \left (\left (4-15 x \right ) \cos \left (3 x \right )-\left (4+15 x \right ) \sin \left (3 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y = {\mathrm e}^{x} \left (\left (7+8 x \right ) \cos \left (2 x \right )+\left (-4 x +8\right ) \sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+8 y^{\prime \prime }+8 y^{\prime }+4 y = -2 \,{\mathrm e}^{x} \left (-\sin \left (x \right )+\cos \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+32 y^{\prime \prime }-64 y^{\prime }+64 y = {\mathrm e}^{2 x} \left (-\sin \left (2 x \right )+\cos \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+26 y^{\prime \prime }-40 y^{\prime }+25 y = {\mathrm e}^{2 x} \left (3 \cos \left (x \right )-\left (1+3 x \right ) \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = {\mathrm e}^{2 x}-4 \,{\mathrm e}^{x}-2 \cos \left (x \right )+4 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 5 \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x}-4 \cos \left (x \right )+4 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime } = -2 x -2+4 \,{\mathrm e}^{x}-6 \,{\mathrm e}^{-x}+96 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+9 y^{\prime }-10 y = 10 \,{\mathrm e}^{2 x}+20 \,{\mathrm e}^{x} \sin \left (2 x \right )-10 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 12 \,{\mathrm e}^{-x}+9 \cos \left (2 x \right )-13 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 4 \,{\mathrm e}^{-x} \left (1-6 x \right )-2 x \cos \left (x \right )+2 \left (1+x \right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = -12 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x}+10 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+11 y^{\prime \prime }-14 y^{\prime }+10 y = -{\mathrm e}^{x} \left (\sin \left (x \right )+2 \cos \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (1+x \right )+{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y = \sinh \left (x \right ) \cos \left (x \right )-\cosh \left (x \right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+9 y^{\prime \prime }+7 y^{\prime }+2 y = {\mathrm e}^{-x} \left (30+24 x \right )-{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y = {\mathrm e}^{x} \left (12 x -2 \cos \left (x \right )+2 \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = {\mathrm e}^{2 x} \left (10+3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-2 y = -{\mathrm e}^{3 x} \left (17 x^{2}+67 x +9\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = {\mathrm e}^{2 x} \left (-3 x^{2}-4 x +5\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = -2 \,{\mathrm e}^{-x} \left (6 x^{2}-18 x +7\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \left (1+x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = -{\mathrm e}^{-x} \left (3 x^{2}-9 x +4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-2 x} \left (\left (23-2 x \right ) \cos \left (x \right )+\left (8-9 x \right ) \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{x} \left (\left (28+6 x \right ) \cos \left (2 x \right )+\left (11-12 x \right ) \sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y = {\mathrm e}^{x} \left (\left (6 x +2\right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{x} \left (1-6 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = -{\mathrm e}^{-x} \left (4-8 x \right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime }-3 y^{\prime }-y = {\mathrm e}^{-\frac {x}{2}} \left (2-3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \left (20-12 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y = 30 \cos \left (x \right )-10 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+5 y^{\prime \prime }-2 y^{\prime } = -2 \,{\mathrm e}^{x} \left (-\sin \left (x \right )+\cos \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 2 x \] |
✓ |
✓ |
|
|
\[ {}4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 x y^{\prime }+2 y = 30 x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 x y^{\prime }+9 y = 96 x^{\frac {5}{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 x y^{\prime }+24 y = x^{4} \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = 12 x^{2} \] |
✓ |
✓ |
|
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\[ {}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 4 x \] |
✓ |
✓ |
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\[ {}x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 x y^{\prime }-18 y = x^{3} \] |
✓ |
✓ |
|
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\[ {}x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+16 x y^{\prime }-16 y = 9 x^{4} \] |
✓ |
✓ |
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\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = \left (1+x \right ) x \] |
✓ |
✓ |
|
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\[ {}x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 9 x^{2} \] |
✓ |
✓ |
|
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\[ {}4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-x y^{\prime }+y = 6 x \] |
✓ |
✓ |
|
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\[ {}x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-6 x y^{\prime }+6 y = 40 x^{3} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = F \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = F \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = F \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = F \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = \sec \left (t \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t \,{\mathrm e}^{2 t} \] |
✓ |
✓ |
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\[ {}2 y^{\prime \prime }-3 y^{\prime }+y = \left (t^{2}+1\right ) {\mathrm e}^{t} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = t \,{\mathrm e}^{3 t}+1 \] |
✓ |
✓ |
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\[ {}3 y^{\prime \prime }+4 y^{\prime }+y = \sin \left (t \right ) {\mathrm e}^{-t} \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = t^{\frac {5}{2}} {\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \sqrt {t +1} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y = f \left (t \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+\frac {t^{2} y}{4} = f \cos \left (t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = t^{2}+1 \] |
✓ |
✓ |
|
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\[ {}m y^{\prime \prime }+c y^{\prime }+k y = F_{0} \cos \left (\omega t \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-4 y = 3 \cos \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y^{\prime }+y = x^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = x \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }-y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-4 y = x +{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-9 y = {\mathrm e}^{3 x}+\sin \left (3 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-6 y = x^{3} \] |
✓ |
✓ |
|
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\[ {}-2 y^{\prime \prime }+3 y = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y = x \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime } = x^{2}+8 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{x} \sin \left (3 x \right ) \] |
✓ |
✓ |
|
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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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\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime } = \left (2 x^{2}+x \right ) {\mathrm e}^{-2 x}+5 \cos \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 8 \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }+4 y = 5 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \] |
✓ |
✓ |
|
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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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\[ {}y^{\prime \prime }+y = {\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+y^{\prime } = 8 \sin \left (2 x \right )+{\mathrm e}^{-x} \] |
✓ |
✓ |
|
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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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\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 4 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 2 x -2 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 3 x +5 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{x}+\sin \left (4 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime } = \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime } = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a^{2} y = \sec \left (x a \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime } = {\mathrm e}^{2 x}+\sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sec \left (x \right ) \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y = {\mathrm e}^{-x} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sec \left (x \right ) \csc \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \csc \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (\frac {x}{3}\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime } = \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{\frac {x}{2}} \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y = 3 \,{\mathrm e}^{-4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{3 x}}{2}-\frac {{\mathrm e}^{-3 x}}{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+3 y^{\prime }-2 y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y = \sin \left (x \right )-{\mathrm e}^{4 x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 4 \,{\mathrm e}^{x}+3 \cos \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = {\mathrm e}^{3 x} \left (1+\sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 n^{2} y^{\prime }+n^{4} y = \sin \left (k x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+4 y = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y = {\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime }-2 y = x^{2}-8 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-y = x^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime } = {\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-y^{\prime } = {\mathrm e}^{x} \left (\sin \left (x \right )-x^{2}\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime } = {\mathrm e}^{2 x} \left (x -3\right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime } = \sin \left (3 x \right )+x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = {\mathrm e}^{2 x} x^{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+2 y^{\prime } = x^{2}+\cos \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }+2 y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = x^{3}-\frac {\cos \left (2 x \right )}{2} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime } = {\mathrm e}^{-2 x} \cos \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{-2 x} \cos \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+2 y^{\prime } = x^{2} \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime \prime }-y = x^{2} \cos \left (x \right ) \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+4 y = x \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = x^{2} \cos \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y = x^{2} \cos \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+4 y^{\prime } = {\mathrm e}^{x}+\sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\left (5\right )}+y^{\prime \prime \prime \prime } = x^{2} \] |
✓ |
✓ |
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\[ {}2 y^{\prime \prime }+3 y^{\prime }-2 y = x^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+y^{\prime } = \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }-y^{\prime } = x \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime } = x \cos \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = x^{2} \cos \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = x^{2} \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y = x \sin \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime } = x^{3} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-y^{\prime } = x \,{\mathrm e}^{2 x} \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-4 y = x \,{\mathrm e}^{2 x} \cos \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+2 y^{\prime } = x^{2} {\mathrm e}^{-x} \sin \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }-18 y = \ln \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = \ln \left (x^{2}\right ) \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{3} \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 1-x \] |
✓ |
✓ |
|
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\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {1}{x} \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 4 x +\sin \left (\ln \left (x \right )\right ) \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = \ln \left (x \right ) x^{2} \] |
✓ |
✓ |
|
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\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+3 y = \left (-1+x \right ) \ln \left (x \right ) \] |
✓ |
✓ |
|
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\[ {}4 x^{3} y^{\prime \prime \prime }+8 x^{2} y^{\prime \prime }-x y^{\prime }+y = x +\ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 x y^{\prime }+10 y = \frac {4}{x^{2}} \] |
✓ |
✓ |
|
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\[ {}x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 x y^{\prime }-6 y = \cos \left (\ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }-x y^{\prime }+4 y = \sin \left (\ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{3} y^{\prime \prime }+4 = 0 \] |
✓ |
✓ |
|
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\[ {}x^{\prime \prime } = \frac {k^{2}}{x^{2}} \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime } = x^{2}+1 \] |
✓ |
✓ |
|
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\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (y^{\prime }+1\right ) = 0 \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }+x = y^{\prime } \] |
✓ |
✓ |
|
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\[ {}x^{\prime \prime }+t x^{\prime } = t^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime } = x y^{\prime }+1 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime } = 1 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime }+1 = {y^{\prime }}^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 {y^{\prime }}^{2} = 2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \sec \left (x \right ) \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime } = {\mathrm e}^{y} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (1+{y^{\prime }}^{2}\right )^{2} = y^{2} y^{\prime \prime } \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \sin \left (y\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \sin \left (x y\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \cos \left (x y\right ) \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }-y = x \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }-y = x \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }-2 x y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-x y^{\prime }+y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}\left (1-2 x \right ) y^{\prime \prime }+4 x y^{\prime }-4 y = x^{2}-x \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x +12\right ) y = x^{2}+x \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }+y = -2 x^{2}+x \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y = -x^{3}+x \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y = x^{4}+x^{2} \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+10 x y^{\prime }+y = -1+x \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = x^{3}+1 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 6 \left (-x^{2}+1\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+2 y = x^{2} \left (2+x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (1+x \right ) y = x \left (x^{2}+x +1\right ) \] |
✓ |
✓ |
|
|
\[ {}\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y = x^{2} \left (1+x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\omega _{0}^{2} x = a \cos \left (\omega t \right ) \] |
✓ |
✓ |
|
|
\[ {}f^{\prime \prime }+2 f^{\prime }+5 f = {\mathrm e}^{-t} \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}f^{\prime \prime }+6 f^{\prime }+9 f = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 4 \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-12 y^{\prime }+16 y = 32 x -8 \] |
✓ |
✓ |
|
|
\[ {}\frac {y^{\prime \prime }}{y}-\frac {{y^{\prime }}^{2}}{y^{2}}+\frac {2 a \coth \left (2 x a \right ) y^{\prime }}{y} = 2 a^{2} \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }+3 \left (1+x \right ) y^{\prime }+y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = x^{n} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}2 y y^{\prime \prime \prime }+2 \left (y+3 y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{2} = \sin \left (x \right ) \] |
✗ |
N/A |
|
|
\[ {}x y^{\prime \prime \prime }+2 y^{\prime \prime } = A x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = {\mathrm e}^{-x^{2}} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 9 x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = x^{n} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime } = 6 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \ln \left (x \right ) x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x} = 9 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 18 \,{\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 4 x^{2}+5 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = 4 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y = 24 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime } = 6 \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 6 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 5 \,{\mathrm e}^{-2 x} x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 8 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y = 4 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 9 \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 2 \,{\mathrm e}^{-x}+3 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 5 \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 9 \,{\mathrm e}^{2 x} x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = -10 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 4 \cos \left (x \right )-2 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\omega ^{2} y = \frac {F_{0} \cos \left (\omega t \right )}{m} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+6 y = 7 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = 4 x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+104 y^{\prime \prime \prime }+2740 y^{\prime \prime } = 5 \,{\mathrm e}^{-2 x} \cos \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y = \sin \left (x \right )^{2} \cos \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-16 y = 20 \cos \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 50 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 10 \,{\mathrm e}^{2 x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 169 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 40 \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 3 \,{\mathrm e}^{x} \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 2 \,{\mathrm e}^{-x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 100 x \,{\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x} \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+10 y = 24 \,{\mathrm e}^{x} \cos \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 34 \,{\mathrm e}^{x}+16 \cos \left (4 x \right )-8 \sin \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 4 \,{\mathrm e}^{3 x} \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 18 \sec \left (3 x \right )^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = \frac {8}{{\mathrm e}^{2 x}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \frac {36}{4-\cos \left (3 x \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = \frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 4 \,{\mathrm e}^{3 x} \sec \left (2 x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right )+4 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \csc \left (x \right )+2 x^{2}+5 x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 2 \tanh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 m y^{\prime }+m^{2} y = \frac {{\mathrm e}^{m x}}{x^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {4 \,{\mathrm e}^{x} \ln \left (x \right )}{x^{3}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = \frac {{\mathrm e}^{-x}}{\sqrt {-x^{2}+4}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+17 y = \frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {4 \,{\mathrm e}^{-2 x}}{x^{2}+1}+2 x^{2}-1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 15 \,{\mathrm e}^{-2 x} \ln \left (x \right )+25 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = \frac {2 \,{\mathrm e}^{x}}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 36 \,{\mathrm e}^{2 x} \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = \frac {2 \,{\mathrm e}^{-x}}{x^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime } = 12 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = F \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = F \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = F \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = F \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 5 \,{\mathrm e}^{2 x} x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 9 \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 8 x \ln \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+6 y = 4 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \frac {x^{2}}{\ln \left (x \right )} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y = x^{m} \ln \left (x \right )^{k} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \csc \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 8 x^{4} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 15 \,{\mathrm e}^{3 x} \sqrt {x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 4 \,{\mathrm e}^{2 x} \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+y = \sqrt {x}\, \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 4 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 4 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime } = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime } = \sin \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y = 8 \,{\mathrm e}^{-x}+1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 5 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 x \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 4 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 5 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 4 \cos \left (2 x \right )+3 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-12 y = 36 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 10 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 \,{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 30 \,{\mathrm e}^{-3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 12 \,{\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 10 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = -6 \,{\mathrm e}^{t}+12 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 6 \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = 13 \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 8 \sin \left (t \right )-6 \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 10 \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 3 \cos \left (t \right )+\sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 9 \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 6 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 7 \sin \left (4 t \right )+14 \cos \left (4 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \operatorname {Heaviside}\left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 1-3 \operatorname {Heaviside}\left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = \operatorname {Heaviside}\left (-1+t \right )-\operatorname {Heaviside}\left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = t -\operatorname {Heaviside}\left (-1+t \right ) \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = -10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 30 \operatorname {Heaviside}\left (-1+t \right ) {\mathrm e}^{1-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 5 \operatorname {Heaviside}\left (t -3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = \delta \left (t -3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -\frac {\pi }{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = \delta \left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 x^{2} y^{\prime }+x y = 2 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }-4 y = 6 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+10 y = 3 x \,{\mathrm e}^{-3 x}-2 \,{\mathrm e}^{3 x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = \left (x +{\mathrm e}^{x}\right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sinh \left (x \right ) \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \cosh \left (x \right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime } = \sin \left (x \right )+x \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y = {\mathrm e}^{2 x} \sin \left (2 x \right )+2 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+3 y^{\prime } = x^{2}+{\mathrm e}^{2 x} x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime } = 7 x -3 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = \sin \left (x \right ) \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 4 \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{i x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 2 \,{\mathrm e}^{2 x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x^{2}+2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x +\sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 4 x \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = x \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-2 x}+x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = x +{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right )+{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (2 x \right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 8 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{x} \left (2 x -3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cot \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 4 x \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \csc \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = \frac {{\mathrm e}^{-x}}{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{-x}\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = x \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = {\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x} \] |
✓ |
✓ |
|
|
\[ {}y^{3} y^{\prime \prime } = k \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime } = {y^{\prime }}^{2}-1 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = x^{2} \] |
✓ |
✓ |
|
|
\[ {}r^{\prime \prime } = -\frac {k}{r^{2}} \] |
✓ |
✓ |
|
|
\[ {}r^{\prime \prime } = \frac {h^{2}}{r^{3}}-\frac {k}{r^{2}} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (y^{\prime }+1\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime } = {\mathrm e}^{y} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = x^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (1+{y^{\prime }}^{2}\right )^{3} = a^{2} {y^{\prime \prime }}^{2} \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+a^{3} x^{2} y = 2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a \,x^{2} y = 1+x \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime }+y = x^{\frac {3}{2}} \] |
✗ |
N/A |
|
|
\[ {}2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = \sqrt {x} \] |
✗ |
N/A |
|
|
\[ {}\left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y = 3 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 10 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 16 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 24 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 12 \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 3 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-16 y = 40 \,{\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 6 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 100 \cos \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+12 y = 80 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+25 y = 120 \sin \left (5 x \right ) \] |
✓ |
✓ |
|
|
\[ {}5 y^{\prime \prime }+12 y^{\prime }+20 y = 120 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 30 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 16 \cos \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+17 y = 60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+5 y = 40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+8 y = 30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}5 y^{\prime \prime }+6 y^{\prime }+2 y = x^{2}+6 x \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+y^{\prime } = 2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 12 x \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 16 \,{\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 8 x \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x^{3}-1+2 \cos \left (x \right )+\left (2-4 x \right ) {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{x}+6 x -5 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \sinh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \sin \left (x \right )+4 x \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 4 \,{\mathrm e}^{x}+\left (1-x \right ) \left ({\mathrm e}^{2 x}-1\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}{y^{\prime \prime }}^{2} = k^{2} \left (1+{y^{\prime }}^{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}k = \frac {y^{\prime \prime }}{\left (y^{\prime }+1\right )^{\frac {3}{2}}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 8 x^{4} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x -\frac {1}{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 2 x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 6 \ln \left (x \right ) x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+y = 3 x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 10 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 4 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 26 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 6 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 5 x +4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 6 \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2}+4 = 0 \] |
✓ |
✓ |
|
|
\[ {}z^{\prime \prime }+x z^{\prime }+z = x^{2}+2 x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+3 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+2 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y \sin \left (x \right ) = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x = F \cos \left (\omega t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 16 \cos \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \cosh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 8 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 10 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+25 y = 5 x^{2}+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }-2 y^{\prime }-y = 2 x -3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = 8 \,{\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-7 y^{\prime }-4 y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 54 x +18 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 100 \sin \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 4 \sinh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 2 \cosh \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+10 y = 20-{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \cos \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = x +{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+3 y = x^{2}-1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = {\mathrm e}^{3 x}+\sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+3 x = {\mathrm e}^{-3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 6 \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-3 x^{\prime }+2 x = \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 3 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+10 y = 50 x \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+2 x^{\prime }+2 x = 85 \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 3 \sin \left (x \right )-4 y \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+5 x^{\prime }+6 x = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 4 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 64 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 50 t^{3}-36 t^{2}-63 t +18 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 2 x \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 9 x^{2}+2 x -1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y = 2 \,{\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = x^{2}-1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 1+{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime } = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = \frac {{\mathrm e}^{x}}{1+{\mathrm e}^{-x}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x = \sin \left (2 t \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N = \ln \left (t \right ) t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime } = 5 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{5}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-60 y^{\prime }-900 y = 5 \,{\mathrm e}^{10 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime } = -3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime } = x^{3} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (x -4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y = 5 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = x^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}q^{\prime \prime }+9 q^{\prime }+14 q = \frac {\sin \left (t \right )}{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 4-x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 2 \left (1-x \right ) {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = x \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+x y^{\prime }-y = 3 x^{4} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2} = 2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 5 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime } = 5 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}-4 y^{\prime \prime \prime } = 5 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime } = x \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = -2 x^{2}+2 x +2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 4 x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \csc \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \csc \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 4 \sec \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = \frac {1}{1+{\mathrm e}^{-x}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = {\mathrm e}^{-x} \sin \left ({\mathrm e}^{-x}\right )+\cos \left ({\mathrm e}^{-x}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y = 2+{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = {\mathrm e}^{x} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = x^{2}+\sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = x +{\mathrm e}^{2 x}-\sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x^{2}+4 x +8 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = -2 \sin \left (x \right )+4 x \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = 2 x^{2}-4 x -1+2 \,{\mathrm e}^{2 x} x^{2}+5 \,{\mathrm e}^{2 x} x +{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{x}+{\mathrm e}^{2 x} x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y = \cos \left (\sqrt {5}\, x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{x}+{\mathrm e}^{-x}+\sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y = x^{3}+x^{2}+{\mathrm e}^{-2 x}+\cos \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-y = {\mathrm e}^{x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 x}}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = x \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{-2 x} \sec \left (x \right )^{2} \left (1+2 \tan \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x +\ln \left (x \right ) x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = \ln \left (x \right )^{2}-\ln \left (x^{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime } = x +\sin \left (\ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+x y^{\prime }-y = 3 x^{4} \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y = \ln \left (1+x \right )^{2}+x -1 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y = 6 x \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 2 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 8 \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+\left (2+x \right ) y = \left (x^{2}+2 x +1\right ) {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+\left (x^{2}+3 x +3\right ) y = \left (-x^{2}+6\right ) {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y = \left (x^{2}-x +1\right ) {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y = \frac {1+x}{x} \] |
✓ |
✓ |
|
|
\[ {}x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}} \] |
✓ |
✓ |
|
|
\[ {}\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right ) = x \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-3 y^{\prime }+\frac {3 y}{x} = 2+x \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-\left (3 x +4\right ) y^{\prime }+3 y = \left (3 x +2\right ) {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+4 x y = 4 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \frac {-x^{2}+1}{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {2}{x^{3}} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = -\frac {2}{x}-\ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime } = x^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y = 8 \] |
✗ |
N/A |
|
|
\[ {}\left (2 y+x \right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+2 y^{\prime } = 2 \] |
✓ |
✓ |
|
|
\[ {}\left (1+2 y+3 y^{2}\right ) y^{\prime \prime \prime }+6 y^{\prime } \left (y^{\prime \prime }+{y^{\prime }}^{2}+3 y y^{\prime \prime }\right ) = x \] |
✗ |
N/A |
|
|
\[ {}3 x \left (y^{2} y^{\prime \prime \prime }+6 y y^{\prime } y^{\prime \prime }+2 {y^{\prime }}^{3}\right )-3 y \left (y y^{\prime \prime }+2 {y^{\prime }}^{2}\right ) = -\frac {2}{x} \] |
✗ |
N/A |
|
|
\[ {}y y^{\prime \prime \prime }+3 y^{\prime } y^{\prime \prime }-2 y y^{\prime \prime }-2 {y^{\prime }}^{2}+y y^{\prime } = {\mathrm e}^{2 x} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+x^{2} y = x^{2}+x +1 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+y^{\prime }-y = 1+x \] |
✓ |
✓ |
|
|
\[ {}x^{3} \left (1+x \right ) y^{\prime \prime \prime }-\left (4 x +2\right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{3} y^{\prime \prime }+y = \frac {1}{x^{4}} \] |
✗ |
N/A |
|
|
\[ {}x y^{\prime \prime }-2 y^{\prime }+y = \cos \left (x \right ) \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-x y = \frac {1}{1-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 10 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+5 y = 29 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 21 \,{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 6 t -8 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y}{25} = \frac {t^{2}}{50} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4} = 9 t^{3}+64 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 50 t -100 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-3 t}-{\mathrm e}^{-5 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+10 y^{\prime }+24 y = 144 t^{2} \] |
✓ |
✓ |
|
|
\[
{}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 |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \delta \left (t -\pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 4 \delta \left (t -3 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+24 y^{\prime }+37 y = 17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 10 \sin \left (t \right )+10 \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = \delta \left (t -\frac {\pi }{2}\right )+\operatorname {Heaviside}\left (t -\pi \right ) \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = \operatorname {Heaviside}\left (-1+t \right )+\delta \left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (t -\pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 2 x \,{\mathrm e}^{x}-1 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime }+x y^{\prime }-y = \cos \left (\frac {1}{x}\right ) \] |
✓ |
✓ |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }-y = x +\frac {1}{x} \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+\left (-2+x \right ) y^{\prime }-y = x^{2}-1 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (3+4 x \right ) y^{\prime }-y = x +\frac {1}{x} \] |
✗ |
N/A |
|
|
\[ {}x^{2} \left (-1+\ln \left (x \right )\right ) y^{\prime \prime }-x y^{\prime }+y = x \left (1-\ln \left (x \right )\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\frac {y}{4} = -\frac {x^{2}}{2}+\frac {1}{2} \] |
✓ |
✓ |
|
|
\[ {}\left (\cos \left (x \right )+\sin \left (x \right )\right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }+\left (-\sin \left (x \right )+\cos \left (x \right )\right ) y = \left (\cos \left (x \right )+\sin \left (x \right )\right )^{2} {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}\left (-\sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) y = \left (-\sin \left (x \right )+\cos \left (x \right )\right )^{2} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 1+3 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{2 x} x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 4 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u = f \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}3 {y^{\prime \prime }}^{2}-y^{\prime } y^{\prime \prime \prime }-y^{\prime \prime } {y^{\prime }}^{2} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 4 \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 \sin \left (t \right )-5 \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = g \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-4 y = f \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 50 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 50 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 2+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime } = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 1+3 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 i y^{\prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x}+2 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \sin \left (2 x \right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}6 y^{\prime \prime }+5 y^{\prime }-6 y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\omega ^{2} y = A \cos \left (\omega x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-8 y = {\mathrm e}^{i x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+16 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 i y^{\prime }-y = {\mathrm e}^{i x}-2 \,{\mathrm e}^{-i x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = x^{2}+\cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = x^{2} {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x \,{\mathrm e}^{x} \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+i y^{\prime }+2 y = 2 \cosh \left (2 x \right )+{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime } = x^{2}+{\mathrm e}^{-x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 \pi y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-2 y^{\prime } = x^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {1}{2 {y^{\prime }}^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\sin \left (y\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\sin \left (y\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}\frac {y^{\prime \prime }}{y^{\prime }} = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime } y^{\prime \prime } = \left (1+x \right ) x \] |
✓ |
✓ |
|
|
\[ {}2 y y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 4 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2} = 1 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-3 y^{\prime } = 5 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-10 y = 6 \,{\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 3 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+10 y^{\prime }+25 y = 14 \,{\mathrm e}^{-5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 25 x^{2}+12 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 20 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 12 x -10 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 6 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 10 x^{4}+2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime } = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \tan \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sec \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cot \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cot \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \left (x^{2}-1\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y = x \left (1+x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2} \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = {\mathrm e}^{2 x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime } = \sin \left (x \right )+24 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 10+42 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-5 y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+4 y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+4 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 2 x -1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-y = x \,{\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sec \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = x \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {2}{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \tan \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 3 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = -8 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = x^{2}+2 x +2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \frac {-1+x}{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = -3 \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\sin \left (y\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }-y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-x^{2} y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 x y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = x^{3}-x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 5 \,{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-5 y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-2 y = -6 \,{\mathrm e}^{\pi -t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-y = t \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+y = 3 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+3 y = 2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+2 y = t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = t \,{\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[
{}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0 |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }-4 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 10 x^{3}-2 x +5 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sqrt {2}\, \sin \left (\sqrt {2}\, t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime \prime }+3 y^{\prime \prime }-3 y^{\prime }-2 y = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} {\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = {\mathrm e}^{t} \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = t +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (t \right ) \operatorname {Heaviside}\left (t -2 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \operatorname {Heaviside}\left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }-y^{\prime } = 2 t^{2} \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+t y^{\prime }-2 y = 10 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (t \right )+t \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = \delta \left (t -2 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 1+\delta \left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -2 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = \delta \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime } = y^{\prime }+x^{5} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -{\mathrm e}^{-2 y} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -{\mathrm e}^{-2 y} \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime } = \sin \left (2 y\right ) \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime } = \sin \left (2 y\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime }-x^{2} y^{\prime } = -x^{2}+3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 2 x +\left (x^{2}-y^{\prime }\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}{y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }+x^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}-1 \] |
✓ |
✓ |
|
|
\[ {}4 y {y^{\prime }}^{2} y^{\prime \prime } = {y^{\prime }}^{4}+3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = -\cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 12 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = x^{2}+2 x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+3 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 4 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+4 y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+4 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }+4 y^{\prime } = t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = f \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = k \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 4 \sin \left (x \right )-4 \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime } = x \] |
✗ |
N/A |
|
|
\[ {}y^{2} y^{\prime \prime } = x \] |
✗ |
N/A |
|
|
\[ {}y^{2} y^{\prime \prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y y^{\prime \prime } = \sin \left (x \right ) \] |
✗ |
N/A |
|
|
\[ {}3 y y^{\prime \prime }+y = 5 \] |
✓ |
✓ |
|
|
\[ {}a y y^{\prime \prime }+b y = c \] |
✓ |
✓ |
|
|
\[ {}a y^{2} y^{\prime \prime }+b y^{2} = c \] |
✓ |
✓ |
|
|
\[ {}a y y^{\prime \prime }+b y = 0 \] |
✓ |
✓ |
|
|
\[ {}z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y y^{\prime } = 2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-2 x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-3 x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{2}-x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{3}+2 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{4}-6 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{5}+24 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x^{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-a x y^{\prime }-b x y-c x = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-x y-x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-x y-x^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-x y-x^{2}-2 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }-x y-x^{2}-4 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-x y-x^{3}+1 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-x y-x^{3}-x^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-x y-x^{3}+2 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-x y-x^{3}+2 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }-x y-x^{3}+2 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }-x y-x^{3}+2 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }-x y-x^{3}+2 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-x y-x^{4}+3 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-x y-x^{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y-x^{3}+2 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y-x^{6}+64 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y-x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y-x^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y-x^{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x y-x^{6}-x^{3}+42 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y-x^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y-x^{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y-x^{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y-x^{4}+2 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 x^{2} y-x^{4}+1 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{3} y-x^{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{3} y-x^{4} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{2} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{3} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-x y-x = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-x y-x^{2} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{3}-x^{2} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}-x y-x^{2}-\frac {1}{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{3} y^{\prime }-x y-x^{3}-x^{2} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = x \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = x \] |
✗ |
N/A |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = x \] |
✓ |
✗ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+y = 8 \sqrt {x}\, \left (1+\ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = 1 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = 1+x \] |
✗ |
N/A |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x \] |
✗ |
N/A |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}+x +1 \] |
✗ |
N/A |
|
|
|
|||
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}+1 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{4} \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \sin \left (x \right ) \] |
✗ |
N/A |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \sin \left (x \right )+1 \] |
✗ |
N/A |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \cos \left (x \right )+\sin \left (x \right ) \] |
✗ |
N/A |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-x y = x^{2}+2 x \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = 1 \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = 1 \] |
✗ |
N/A |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}+\cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{3}+\cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{3} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{3} \cos \left (x \right )+\sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = x \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = \sin \left (x \right ) \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = x^{3}+x \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}\frac {x y^{\prime \prime }}{1-x}+y = \frac {1}{1-x} \] |
✓ |
✓ |
|
|
\[ {}\frac {x y^{\prime \prime }}{1-x}+y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+20 y^{\prime }+500 y = 100000 \cos \left (100 x \right ) \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y = 6 x^{3} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {1}{x} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \frac {1}{x} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+y = \frac {1}{x} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \frac {1}{x} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-24 y = 16-\left (2+x \right ) {\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = {\mathrm e}^{\cos \left (x \right ) a} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+{\mathrm e}^{y} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}{y^{\prime \prime }}^{2} = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = x \] |
✓ |
✓ |
|
|
\[ {}{y^{\prime \prime }}^{2} = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}{y^{\prime \prime }}^{2}+y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2} = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x \] |
✓ |
✓ |
|
|
\[ {}{y^{\prime \prime }}^{2}+y^{\prime } = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2} = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = 1+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = x^{2}+x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = x^{3}+x^{2}+x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 1+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x^{2}+x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x^{3}+x^{2}+x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 1+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x^{2}+x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x^{3}+x^{2}+x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{3} {y^{\prime \prime }}^{2}+y y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y {y^{\prime \prime }}^{3}+y^{3} y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {2 y}{x^{2}} = x \,{\mathrm e}^{-\sqrt {x}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = x \] |
✓ |
✓ |
|
|
\[ {}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 2 x^{3}-x^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 4 \cos \left (\ln \left (1+x \right )\right ) \] |
✗ |
N/A |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 8 x^{3} \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5} \] |
✓ |
✓ |
|
|
\[ {}\cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 y \cos \left (x \right )^{3} = 2 \cos \left (x \right )^{5} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x} = 4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = x^{1+m} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y = {\mathrm e}^{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = {\mathrm e}^{x^{2}} \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y = x \,{\mathrm e}^{x}+3 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime }+a \phi ^{\prime }\left (x \right ) y^{3}+6 a \phi \left (x \right ) y^{2}+\frac {\left (2 a +1\right ) y \phi ^{\prime \prime }\left (x \right )}{\phi ^{\prime }\left (x \right )}+2+2 a = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+y-\sin \left (n x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y-a \cos \left (b x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y-\sin \left (x a \right ) \sin \left (b x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y-4 x^{2} {\mathrm e}^{x^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a^{2} y-\cot \left (x a \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\left (\frac {p^{\prime \prime \prime \prime }\left (x \right )}{30}+\frac {7 p^{\prime \prime }\left (x \right )}{3}+a p \left (x \right )+b \right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+b y-f \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y-{\mathrm e}^{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y-{\mathrm e}^{x^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } \sqrt {x}+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{\frac {3}{2}}}{3}} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\left (2 \,{\mathrm e}^{x}+1\right ) y^{\prime }+{\mathrm e}^{2 x} y-{\mathrm e}^{3 x} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+\tan \left (x \right )+b y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+f \left (x \right ) y^{\prime }+\left (f^{\prime }\left (x \right )+a \right ) y-g \left (x \right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+\frac {f \left (x \right ) f^{\prime \prime \prime }\left (x \right ) y^{\prime }}{f \left (x \right )^{2}+b^{2}}-\frac {a^{2} {f^{\prime }\left (x \right )}^{2} y}{f \left (x \right )^{2}+b^{2}} = 0 \] |
✗ |
N/A |
|
|
\[ {}x \left (y^{\prime \prime }+y\right )-\cos \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }-x y-{\mathrm e}^{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-x y^{\prime }-y-x \left (1+x \right ) {\mathrm e}^{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (4 x^{2}-1\right ) y^{\prime }-4 x^{3} y-4 x^{5} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+\frac {y}{\ln \left (x \right )}-x \,{\mathrm e}^{x} \left (x \ln \left (x \right )+2\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y-x^{2} a = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-v^{2}+x^{2}\right ) y-f \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y-3 x^{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y-x^{5} \ln \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y-x \sin \left (x \right )-\left (x^{2} a +12 a +4\right ) \cos \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y-\frac {x^{2}}{\cos \left (x \right )} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y-\frac {x^{3}}{\cos \left (x \right )} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (-v^{2}+x^{2}+1\right ) y-f \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y-5 x = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y-\ln \left (x \right ) x^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y-x^{4}+x^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y-\sin \left (x \right ) x^{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-2 \cos \left (x \right )+2 x = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-n \left (n +1\right ) y+\frac {\partial }{\partial x}\operatorname {LegendreP}\left (n , x\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+2 = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-a = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+\left (\left (\operatorname {a1} +\operatorname {b1} +1\right ) x -\operatorname {d1} \right ) y^{\prime }+\operatorname {a1} \operatorname {b1} \operatorname {d1} = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{\frac {7}{3}} = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (4 x^{2}+1\right ) y-4 \sqrt {x^{3}}\, {\mathrm e}^{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+5 x y^{\prime }-y-\ln \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x^{2} \ln \left (x \right ) y^{\prime }+\left (x^{2} \ln \left (x \right )^{2}+2 x -8\right ) y-4 x^{2} \sqrt {{\mathrm e}^{x} x^{-x}} = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y-3 x -1 = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (3 x -1\right )^{2} y^{\prime \prime }+3 \left (3 x -1\right ) y^{\prime }-9 y-\ln \left (3 x -1\right )^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime }-x^{2} y^{\prime }+x y-\ln \left (x \right )^{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }+x y-1 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (2 x a +b \right ) y^{\prime }}{x \left (x a +b \right )}-\frac {\left (a v x -b \right ) y}{\left (x a +b \right ) x^{2}}+A x \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime } = -\frac {b y}{x^{2} \left (x -a \right )^{2}}+c \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = -\frac {\sin \left (x \right ) y^{\prime }}{\cos \left (x \right )}-\frac {\left (2 x^{2}+x^{2} \sin \left (x \right )^{2}-24 \cos \left (x \right )^{2}\right ) y}{4 x^{2} \cos \left (x \right )^{2}}+\sqrt {\cos \left (x \right )} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime }+y a \,x^{3}-b x = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime }-a^{2} y^{\prime }-{\mathrm e}^{2 x a} \sin \left (x \right )^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+\left (a +b -1\right ) x y^{\prime }-y a b = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime }+x^{2 c -2} y^{\prime }+\left (c -1\right ) x^{2 c -3} y = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime }-3 \left (2 \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )+a \right ) y^{\prime }+b y = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime }+\left (-n^{2}+1\right ) \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y^{\prime }+\frac {\left (\left (-n^{2}+1\right ) \operatorname {WeierstrassPPrime}\left (x , \operatorname {g2} , \operatorname {g3}\right )-a \right ) y}{2} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime }-\left (4 n \left (n +1\right ) \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )+a \right ) y^{\prime }-2 n \left (n +1\right ) \operatorname {WeierstrassPPrime}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime }-\left (3 k^{2} \operatorname {JacobiSN}\left (z , x\right )^{2}+a \right ) y^{\prime }+\left (b +c \operatorname {JacobiSN}\left (z , x\right )^{2}-3 k^{2} \operatorname {JacobiSN}\left (z , x\right ) \operatorname {JacobiCN}\left (z , x\right ) \operatorname {JacobiDN}\left (z , x\right )\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime }-\left (6 k^{2} \sin \left (x \right )^{2}+a \right ) y^{\prime }+b y = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-a^{2} y^{\prime }+2 a^{2} y-\sinh \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-a^{3} y-{\mathrm e}^{x a} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 x y^{\prime \prime }+2 \left (4 x^{2}+2 a -1\right ) y^{\prime }-8 a x y = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime } \sin \left (x \right )-2 \cos \left (x \right ) y^{\prime }+y \sin \left (x \right )-\ln \left (x \right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime }+f \left (x \right ) \left (x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}4 y^{\prime \prime \prime }-8 y^{\prime \prime }-11 y^{\prime }-3 y+18 \,{\mathrm e}^{x} = 0 \] |
✓ |
✓ |
|
|
\[ {}27 y^{\prime \prime \prime }-36 n^{2} \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y^{\prime }-2 n \left (n +3\right ) \left (4 n -3\right ) \operatorname {WeierstrassPPrime}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x y^{\prime \prime \prime }-\left (x +2 v \right ) y^{\prime \prime }-\left (x -2 v -1\right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-f \left (x \right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}2 x y^{\prime \prime \prime }+3 y^{\prime \prime }+a x y-b = 0 \] |
✗ |
N/A |
|
|
\[ {}2 x y^{\prime \prime \prime }-4 \left (x +\nu -1\right ) y^{\prime \prime }+\left (2 x +6 \nu -5\right ) y^{\prime }+\left (1-2 \nu \right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}2 x y^{\prime \prime \prime }+3 \left (2 x a +k \right ) y^{\prime \prime }+6 \left (a k +b x \right ) y^{\prime }+\left (3 b k +2 c x \right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}\left (-2+x \right ) x y^{\prime \prime \prime }-\left (-2+x \right ) x y^{\prime \prime }-2 y^{\prime }+2 y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime \prime }+3 x y^{\prime \prime }+\left (4 a^{2} x^{2 a}+1-4 \nu ^{2} a^{2}\right ) y^{\prime } = 4 a^{3} x^{2 a -1} y \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-3 \left (x -m \right ) x y^{\prime \prime }+\left (2 x^{2}+4 \left (n -m \right ) x +m \left (2 m -1\right )\right ) y^{\prime }-2 n \left (2 x -2 m +1\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime \prime }+4 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }+3 x y-f \left (x \right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime }-\ln \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-3 \left (p +q \right ) x y^{\prime \prime }+3 p \left (3 q +1\right ) y^{\prime }-x^{2} y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-2 \left (n +1\right ) x y^{\prime \prime }+\left (x^{2} a +6 n \right ) y^{\prime }-2 a x y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-\left (x^{2}-2 x \right ) y^{\prime \prime }-\left (x^{2}+\nu ^{2}-\frac {1}{4}\right ) y^{\prime }+\left (x^{2}-2 x +\nu ^{2}-\frac {1}{4}\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-\left (x +\nu \right ) x y^{\prime \prime }+\nu \left (2 x +1\right ) y^{\prime }-\nu \left (1+x \right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-2 \left (x^{2}-x \right ) y^{\prime \prime }+\left (x^{2}-2 x +\frac {1}{4}-\nu ^{2}\right ) y^{\prime }+\left (\nu ^{2}-\frac {1}{4}\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-\left (x^{4}-6 x \right ) y^{\prime \prime }-\left (2 x^{3}-6\right ) y^{\prime }+2 x^{2} y = 0 \] |
✗ |
N/A |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime \prime }+8 x y^{\prime \prime }+10 y^{\prime }-3+\frac {1}{x^{2}}-2 \ln \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}2 x \left (-1+x \right ) y^{\prime \prime \prime }+3 \left (2 x -1\right ) y^{\prime \prime }+\left (2 x a +b \right ) y^{\prime }+a y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+\left (-\nu ^{2}+1\right ) x y^{\prime }+\left (a \,x^{3}+\nu ^{2}-1\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+\left (4 x^{3}+\left (-4 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (4 \nu ^{2}-1\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+\left (a \,x^{2 \nu }+1-\nu ^{2}\right ) x y^{\prime }+\left (b \,x^{3 \nu }+a \left (\nu -1\right ) x^{2 \nu }+\nu ^{2}-1\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y-6 x^{3} \left (-1+x \right ) \ln \left (x \right )+x^{3} \left (x +8\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+\left (-a^{2}+1\right ) x y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+\left (x^{2}+8\right ) x y^{\prime }-2 \left (x^{2}+4\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 \left (1-a \right ) x^{2} y^{\prime \prime }+\left (4 b^{2} c^{2} x^{2 c +1}+1-4 \nu ^{2} c^{2}+3 a \left (a -1\right ) x \right ) y^{\prime }+\left (4 b^{2} c^{2} \left (c -a \right ) x^{2 c}+a \left (4 \nu ^{2} c^{2}-a^{2}\right )\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+\left (x +3\right ) x^{2} y^{\prime \prime }+5 \left (x -6\right ) x y^{\prime }+\left (4 x +30\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+\ln \left (x \right )+2 x y^{\prime }-y-2 x^{3} = 0 \] |
✓ |
✗ |
|
|
\[ {}\left (x^{2}+1\right ) x y^{\prime \prime \prime }+3 \left (2 x^{2}+1\right ) y^{\prime \prime }-12 y = 0 \] |
✗ |
N/A |
|
|
\[ {}\left (x +3\right ) x^{2} y^{\prime \prime \prime }-3 x \left (2+x \right ) y^{\prime \prime }+6 \left (1+x \right ) y^{\prime }-6 y = 0 \] |
✗ |
N/A |
|
|
\[ {}2 \left (x -\operatorname {a1} \right ) \left (x -\operatorname {a2} \right ) \left (x -\operatorname {a3} \right ) y^{\prime \prime \prime }+\left (9 x^{2}-6 \left (\operatorname {a1} +\operatorname {a2} +\operatorname {a3} \right ) x +3 \operatorname {a1} \operatorname {a2} +3 \operatorname {a1} \operatorname {a3} +3 \operatorname {a2} \operatorname {a3} \right ) y^{\prime \prime }-2 \left (\left (n^{2}+n -3\right ) x +b \right ) y^{\prime }-n \left (n +1\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}\left (1+x \right ) x^{3} y^{\prime \prime \prime }-\left (4 x +2\right ) x^{2} y^{\prime \prime }+\left (10 x +4\right ) x y^{\prime }-4 \left (1+3 x \right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}4 x^{4} y^{\prime \prime \prime }-4 x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }-1 = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) x^{3} y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-4 \left (3 x^{2}+1\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} \left (x^{4}+2 x^{2}+2 x +1\right ) y^{\prime \prime \prime }-\left (2 x^{6}+3 x^{4}-6 x^{2}-6 x -1\right ) y^{\prime \prime }+\left (x^{6}-6 x^{3}-15 x^{2}-12 x -2\right ) y^{\prime }+\left (x^{4}+4 x^{3}+8 x^{2}+6 x +1\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}\left (x -a \right )^{3} \left (-b +x \right )^{3} y^{\prime \prime \prime }-c y = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime } \sin \left (x \right )+\left (2 \cos \left (x \right )+1\right ) y^{\prime \prime }-\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}\left (x +\sin \left (x \right )\right ) y^{\prime \prime \prime }+3 \left (\cos \left (x \right )+1\right ) y^{\prime \prime }-3 \sin \left (x \right ) y^{\prime }-y \cos \left (x \right )+\sin \left (x \right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime } \sin \left (x \right )^{2}+3 y^{\prime \prime } \sin \left (x \right ) \cos \left (x \right )+\left (\cos \left (2 x \right )+4 \nu \left (\nu +1\right ) \sin \left (x \right )^{2}\right ) y^{\prime }+2 \nu \left (\nu +1\right ) y \sin \left (2 x \right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}f^{\prime }\left (x \right ) y^{\prime \prime }+f \left (x \right ) y^{\prime \prime \prime }+g^{\prime }\left (x \right ) y^{\prime }+g \left (x \right ) y^{\prime \prime }+h^{\prime }\left (x \right ) y+h \left (x \right ) y^{\prime }+A \left (x \right ) \left (f \left (x \right ) y^{\prime \prime }+g \left (x \right ) y^{\prime }+h \left (x \right ) y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y-f = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-12 y^{\prime \prime }+12 y-16 x^{4} {\mathrm e}^{x^{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y-\cosh \left (x a \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+\left (\lambda +1\right ) a^{2} y^{\prime \prime }+\lambda \,a^{4} y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+a \left (b x -1\right ) y^{\prime \prime }+a b y^{\prime }+\lambda y = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime \prime }+a \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y^{\prime \prime }+b \operatorname {WeierstrassPPrime}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y^{\prime }+\left (c \left (6 \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )^{2}-\frac {\operatorname {g2}}{2}\right )+d \right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime \prime }-\left (12 k^{2} \operatorname {JacobiSN}\left (z , x\right )^{2}+a \right ) y^{\prime \prime }+b y^{\prime }+\left (\alpha \operatorname {JacobiSN}\left (z , x\right )^{2}+\beta \right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y-32 \sin \left (2 x \right )+24 \cos \left (2 x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+11 y^{\prime \prime }-3 y^{\prime }-4 \cos \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime } x +5 y^{\prime \prime \prime }-24 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime } x -\left (6 x^{2}+1\right ) y^{\prime \prime \prime }+12 x^{3} y^{\prime \prime }-\left (9 x^{2}-7\right ) x^{2} y^{\prime }+2 \left (x^{2}-3\right ) x^{3} y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }-2 \left (\nu ^{2} x^{2}+6\right ) y^{\prime \prime }+\nu ^{2} \left (\nu ^{2} x^{2}+4\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }+2 x y^{\prime \prime \prime }+a y-b \,x^{2} = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }+\left (2 n -2 \nu +4\right ) x y^{\prime \prime \prime }+\left (n -\nu +1\right ) \left (n -\nu +2\right ) y^{\prime \prime }-\frac {b^{4} y}{16} = 0 \] |
✗ |
N/A |
|
|
|
|||
|
\[ {}x^{4} y^{\prime \prime \prime \prime }-2 n \left (n +1\right ) x^{2} y^{\prime \prime }+4 n \left (n +1\right ) x y^{\prime }+\left (a \,x^{4}+n \left (n +1\right ) \left (n +3\right ) \left (n -2\right )\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }+\left (4 n^{2}-1\right ) x y^{\prime }-4 y x^{4} = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }-\left (4 n^{2}-1\right ) x y^{\prime }+\left (-4 x^{4}+4 n^{2}-1\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}+3\right ) x^{2} y^{\prime \prime }+\left (12 n^{2}-3\right ) x y^{\prime }-\left (4 x^{4}+12 n^{2}-3\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-\rho ^{2}-\sigma ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-\rho ^{2}-\sigma ^{2}+1\right ) x \right ) y^{\prime }+\left (\rho ^{2} \sigma ^{2}+8 x^{2}\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-2 \mu ^{2}-2 \nu ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-2 \mu ^{2}-2 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (8 x^{2}+\left (\mu ^{2}-\nu ^{2}\right )^{2}\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a \right ) x^{3} y^{\prime \prime \prime }+\left (4 b^{2} c^{2} x^{2 c}+6 \left (a -1\right )^{2}-2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )+1\right ) x^{2} y^{\prime \prime }+\left (4 \left (3 c -2 a +1\right ) b^{2} c^{2} x^{2 c}+\left (2 a -1\right ) \left (2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )-2 a \left (a -1\right )-1\right )\right ) x y^{\prime }+\left (4 \left (a -c \right ) \left (-2 c +a \right ) b^{2} c^{2} x^{2 c}+\left (c \mu +c \nu +a \right ) \left (c \mu +c \nu -a \right ) \left (c \mu -c \nu +a \right ) \left (c \mu -c \nu -a \right )\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a -4 c \right ) x^{3} y^{\prime \prime \prime }+\left (-2 \nu ^{2} c^{2}+2 a^{2}+4 \left (a +c -1\right )^{2}+4 \left (a -1\right ) \left (c -1\right )-1\right ) x^{2} y^{\prime \prime }+\left (2 \nu ^{2} c^{2}-2 a^{2}-\left (2 a -1\right ) \left (2 c -1\right )\right ) \left (2 a +2 c -1\right ) x y^{\prime }+\left (\left (-\nu ^{2} c^{2}+a^{2}\right ) \left (-\nu ^{2} c^{2}+a^{2}+4 a c +4 c^{2}\right )-b^{4} c^{4} x^{4 c}\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}\nu ^{4} x^{4} y^{\prime \prime \prime \prime }+\left (4 \nu -2\right ) \nu ^{3} x^{3} y^{\prime \prime \prime }+\left (\nu -1\right ) \left (2 \nu -1\right ) \nu ^{2} x^{2} y^{\prime \prime }-\frac {b^{4} x^{\frac {2}{\nu }} y}{16} = 0 \] |
✗ |
N/A |
|
|
\[ {}\left (x^{2}-1\right )^{2} y^{\prime \prime \prime \prime }+10 x \left (x^{2}-1\right ) y^{\prime \prime \prime }+\left (24 x^{2}-8-2 \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )\right ) \left (x^{2}-1\right )\right ) y^{\prime \prime }-6 x \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )-2\right ) y^{\prime }+\left (\left (\mu \left (\mu +1\right )-\nu \left (\nu +1\right )\right )^{2}-2 \mu \left (\mu +1\right )-2 \nu \left (\nu +1\right )\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}\left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \,{\mathrm e}^{x} y^{\prime }+{\mathrm e}^{x} y-\frac {1}{x^{5}} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime \prime } \sin \left (x \right )^{4}+2 y^{\prime \prime \prime } \sin \left (x \right )^{3} \cos \left (x \right )+y^{\prime \prime } \sin \left (x \right )^{2} \left (\sin \left (x \right )^{2}-3\right )+y^{\prime } \sin \left (x \right ) \cos \left (x \right ) \left (2 \sin \left (x \right )^{2}+3\right )+\left (a^{4} \sin \left (x \right )^{4}-3\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime \prime } \sin \left (x \right )^{6}+4 y^{\prime \prime \prime } \sin \left (x \right )^{5} \cos \left (x \right )-6 y^{\prime \prime } \sin \left (x \right )^{6}-4 y^{\prime } \sin \left (x \right )^{5} \cos \left (x \right )+y \sin \left (x \right )^{6}-f = 0 \] |
✗ |
N/A |
|
|
\[ {}f \left (y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y\right )+2 \operatorname {df} \left (y^{\prime \prime \prime }-a^{2} y^{\prime }\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y-\lambda \left (x a -b \right ) \left (y^{\prime \prime }-a^{2} y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime }-x a -b \sin \left (x \right )-c \cos \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (6\right )}+y-\sin \left (\frac {3 x}{2}\right ) \sin \left (\frac {x}{2}\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}-a x y-b = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\left (5\right )}+a \,x^{\nu } y^{\prime }+a \nu \,x^{\nu -1} y = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\left (5\right )}+a y^{\prime \prime \prime \prime }-f = 0 \] |
✓ |
✓ |
|
|
\[ {}x \left (a y^{\prime }+b y^{\prime \prime }+c y^{\prime \prime \prime }+e y^{\prime \prime \prime \prime }\right ) y = 0 \] |
✗ |
N/A |
|
|
\[ {}x y^{\left (5\right )}-\left (a A_{1} -A_{0} \right ) x -A_{1} -\left (\left (a A_{2} -A_{1} \right ) x +A_{2} \right ) y^{\prime } = 0 \] |
✗ |
N/A |
|
|
\[ {}\left (x -a \right )^{5} \left (-b +x \right )^{5} y^{\left (5\right )}-c y = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-6 y^{2}-x = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+a y^{2}+b x +c = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-2 y^{3}-x y+a = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-2 a^{2} y^{3}+2 a b x y-b = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+d +b x y+c y+a y^{3} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+d +b y^{2}+c y+a y^{3} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\frac {1}{\left (a y^{2}+b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{\frac {3}{2}}} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-{\mathrm e}^{y} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+a \sin \left (y\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta \sin \left (x \right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime } = \frac {f \left (\frac {y}{\sqrt {x}}\right )}{x^{\frac {3}{2}}} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-\frac {\left (3 n +4\right ) y^{\prime }}{n}-\frac {2 \left (n +1\right ) \left (n +2\right ) y \left (y^{\frac {n}{n +1}}-1\right )}{n^{2}} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+y y^{\prime }-y^{3}-\left (\frac {f^{\prime }\left (x \right )}{f \left (x \right )}+f \left (x \right )\right ) \left (3 y^{\prime }+y^{2}\right )+\left (a f \left (x \right )^{2}+3 f^{\prime }\left (x \right )+\frac {3 {f^{\prime }\left (x \right )}^{2}}{f \left (x \right )^{2}}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}\right ) y+b f \left (x \right )^{3} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+2 y y^{\prime }+f \left (x \right ) \left (y^{\prime }+y^{2}\right )-g \left (x \right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+3 y y^{\prime }+y^{3}+f \left (x \right ) y-g \left (x \right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-3 y y^{\prime }-3 a y^{2}-4 a^{2} y-b = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+f \left (x , y\right ) y^{\prime }+g \left (x , y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+a {y^{\prime }}^{2}+b \sin \left (y\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b \sin \left (y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-\frac {D\left (f \right )\left (y\right ) {y^{\prime }}^{3}}{f \left (y\right )}+g \left (x \right ) y^{\prime }+h \left (x \right ) f \left (y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+\phi \left (y\right ) {y^{\prime }}^{2}+f \left (x \right ) y^{\prime }+g \left (x \right ) \Phi \left (y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+f \left (y\right ) {y^{\prime }}^{2}+g \left (y\right ) y^{\prime }+h \left (y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+\left (1+{y^{\prime }}^{2}\right ) \left (f \left (x , y\right ) y^{\prime }+g \left (x , y\right )\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-a \left (-y+x y^{\prime }\right )^{v} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+\left (y^{\prime }-\frac {y}{x}\right )^{a} f \left (x , y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}+b \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = a \sqrt {{y^{\prime }}^{2}+b y^{2}} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime } = a \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 a x \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 2 a \left (c +b x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \] |
✗ |
N/A |
|
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\[ {}y^{\prime \prime }-f \left (y^{\prime }, x a +b y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-x^{n -2} f \left (y x^{-n}, y^{\prime } x^{-n +1}\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}a y^{\prime \prime }+h \left (y^{\prime }\right )+c y = 0 \] |
✗ |
N/A |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x \,{\mathrm e}^{y} = 0 \] |
✗ |
N/A |
|
|
\[ {}x y^{\prime \prime }+a y^{\prime }+b x \,{\mathrm e}^{y} = 0 \] |
✗ |
N/A |
|
|
\[ {}x y^{\prime \prime }+a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y} = 0 \] |
✗ |
N/A |
|
|
\[ {}x y^{\prime \prime }+a \left (-y+x y^{\prime }\right )^{2}-b = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (1+a \right ) x y^{\prime }-x^{k} f \left (x^{k} y, x y^{\prime }+k y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime }+a \left (-y+x y^{\prime }\right )^{2}-b \,x^{2} = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime }+a y {y^{\prime }}^{2}+b x = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime }-\sqrt {a \,x^{2} {y^{\prime }}^{2}+b y^{2}} = 0 \] |
✗ |
N/A |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )+12 x y+24 = 0 \] |
✗ |
N/A |
|
|
\[ {}2 x^{3} y^{\prime \prime }+x^{2} \left (9+2 x y\right ) y^{\prime }+b +x y \left (a +3 x y-2 x^{2} y^{2}\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}2 \left (-x^{k}+4 x^{3}\right ) \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )-\left (k \,x^{k -1}-12 x^{2}\right ) \left (3 y^{\prime }+y^{2}\right )+a x y+b = 0 \] |
✗ |
N/A |
|
|
\[ {}\left (x^{2} a +b x +c \right )^{\frac {3}{2}} y^{\prime \prime }-F \left (\frac {y}{\sqrt {x^{2} a +b x +c}}\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{\frac {n}{n +1}} y^{\prime \prime }-y^{\frac {2 n +1}{n +1}} = 0 \] |
✗ |
N/A |
|
|
\[ {}f \left (x \right )^{2} y^{\prime \prime }+f \left (x \right ) f^{\prime }\left (x \right ) y^{\prime }-h \left (y, f \left (x \right ) y^{\prime }\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y y^{\prime \prime }-a = 0 \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime }-x a = 0 \] |
✗ |
N/A |
|
|
\[ {}y y^{\prime \prime }-x^{2} a = 0 \] |
✗ |
N/A |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2}-a = 0 \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime }+y^{2}-x a -b = 0 \] |
✗ |
N/A |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0 \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0 \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y y^{\prime \prime }+a \left (1+{y^{\prime }}^{2}\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}-1-2 a y \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } \left (x -y\right )-\left (y^{\prime }+1\right ) \left (1+{y^{\prime }}^{2}\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime } \left (x -y\right )-h \left (y^{\prime }\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}2 y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}+a = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}+y^{2} f \left (x \right )+a = 0 \] |
✗ |
N/A |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3} = 0 \] |
✗ |
N/A |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}+b -4 \left (x^{2}+a \right ) y^{2}-8 x y^{3}-3 y^{4} = 0 \] |
✗ |
N/A |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}+4 y^{2} y^{\prime }+1+y^{2} f \left (x \right )+y^{4} = 0 \] |
✗ |
N/A |
|
|
\[ {}2 \left (y-a \right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y y^{\prime \prime }-2 {y^{\prime }}^{2}-x^{2} a -b x -c = 0 \] |
✗ |
N/A |
|
|
\[ {}a y y^{\prime \prime }+b {y^{\prime }}^{2}+\operatorname {c4} y^{4}+\operatorname {c3} y^{3}+\operatorname {c2} y^{2}+\operatorname {c1} y+\operatorname {c0} = 0 \] |
✓ |
✓ |
|
|
\[ {}x y y^{\prime \prime }+x {y^{\prime }}^{2}+a y y^{\prime }+f \left (x \right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime }+x \left (d +a y^{4}\right )+y \left (c +b y^{2}\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}2 x^{2} y y^{\prime \prime }-x^{2} \left (1+{y^{\prime }}^{2}\right )+y^{2} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{2} y^{\prime \prime }-a = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}+x a = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-x a -b = 0 \] |
✗ |
N/A |
|
|
\[ {}2 y \left (1-y\right ) y^{\prime \prime }-\left (-3 y+1\right ) {y^{\prime }}^{2}+h \left (y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}-2 y \left (1-y\right ) y^{\prime \prime }+\left (-3 y+1\right ) {y^{\prime }}^{2}-4 y y^{\prime } \left (f \left (x \right ) y+g \left (x \right )\right )+\left (1-y\right )^{3} \left (\operatorname {f0} \left (x \right )^{2} y^{2}-\operatorname {f1} \left (x \right )^{2}\right )+4 y^{2} \left (1-y\right ) \left (f \left (x \right )^{2}-g \left (x \right )^{2}-g^{\prime }\left (x \right )-f^{\prime }\left (x \right )\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}3 y \left (1-y\right ) y^{\prime \prime }-2 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}\left (1-y\right ) y^{\prime \prime }-3 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}a y \left (y-1\right ) y^{\prime \prime }+\left (b y+c \right ) {y^{\prime }}^{2}+h \left (y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}x y^{2} y^{\prime \prime }-a = 0 \] |
✗ |
N/A |
|
|
\[ {}2 x^{2} y \left (y-1\right ) y^{\prime \prime }-x^{2} \left (3 y-1\right ) {y^{\prime }}^{2}+2 x y \left (y-1\right ) y^{\prime }+\left (a y^{2}+b \right ) \left (y-1\right )^{3}+c x y^{2} \left (y-1\right )+d \,x^{2} y^{2} \left (y+1\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{3} y^{\prime \prime }-a = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1 = 0 \] |
✗ |
N/A |
|
|
\[ {}2 y^{3} y^{\prime \prime }+y^{2} {y^{\prime }}^{2}-x^{2} a -b x -c = 0 \] |
✗ |
N/A |
|
|
\[ {}2 \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) y^{\prime \prime }-\left (\left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )+\left (y-b \right ) \left (y-c \right )\right ) {y^{\prime }}^{2}+\left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} \left (A_{0} +\frac {B_{0}}{\left (y-a \right )^{2}}+\frac {C_{1}}{\left (y-b \right )^{2}}+\frac {D_{0}}{\left (y-c \right )^{2}}\right ) = 0 \] |
✓ |
✗ |
|
|
\[ {}-2 x y \left (1-x \right ) \left (1-y\right ) \left (x -y\right ) y^{\prime \prime }+x \left (1-x \right ) \left (x -2 x y-2 y+3 y^{2}\right ) {y^{\prime }}^{2}+2 y \left (1-y\right ) \left (x^{2}+y-2 x y\right ) y^{\prime }-y^{2} \left (1-y\right )^{2}-f \left (y \left (y-1\right ) \left (y-x \right )\right )^{\frac {3}{2}} = 0 \] |
✗ |
N/A |
|
|
\[ {}2 x^{2} y \left (1-x \right )^{2} \left (1-y\right ) \left (x -y\right ) y^{\prime \prime }-x^{2} \left (1-x \right )^{2} \left (x -2 x y-2 y+3 y^{2}\right ) {y^{\prime }}^{2}-2 x y \left (1-x \right ) \left (1-y\right ) \left (x^{2}+y-2 x y\right ) y^{\prime }+b x \left (1-y\right )^{2} \left (x -y\right )^{2}-c \left (1-x \right ) y^{2} \left (x -y\right )^{2}-d x y^{2} \left (1-x \right ) \left (1-y\right )^{2}+a y^{2} \left (x -y\right )^{2} \left (1-y\right )^{2} = 0 \] |
✗ |
N/A |
|
|
\[ {}\sqrt {y}\, y^{\prime \prime }-a = 0 \] |
✓ |
✓ |
|
|
\[ {}\sqrt {x^{2}+y^{2}}\, y^{\prime \prime }-a \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} = 0 \] |
✗ |
N/A |
|
|
\[ {}h \left (y\right ) y^{\prime \prime }+a D\left (h \right )\left (y\right ) {y^{\prime }}^{2}+j \left (y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}h \left (y\right ) y^{\prime \prime }-D\left (h \right )\left (y\right ) {y^{\prime }}^{2}-h \left (y\right )^{2} j \left (x , \frac {y^{\prime }}{h \left (y\right )}\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}\left (-y+x y^{\prime }\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right )^{2} = 0 \] |
✗ |
N/A |
|
|
\[ {}\left ({y^{\prime }}^{2}+a \left (-y+x y^{\prime }\right )\right ) y^{\prime \prime }-b = 0 \] |
✗ |
N/A |
|
|
\[ {}\left (a \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }\right ) y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0 \] |
✓ |
✓ |
|
|
\[ {}h \left (y^{\prime }\right ) y^{\prime \prime }+j \left (y\right ) y^{\prime }+f = 0 \] |
✗ |
N/A |
|
|
\[ {}{y^{\prime \prime }}^{2}-a y-b = 0 \] |
✓ |
✓ |
|
|
\[ {}y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x} = 0 \] |
✗ |
N/A |
|
|
\[ {}\sqrt {a {y^{\prime \prime }}^{2}+b {y^{\prime }}^{2}}+c y y^{\prime \prime }+d {y^{\prime }}^{2} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime }-a^{2} \left ({y^{\prime }}^{5}+2 {y^{\prime }}^{3}+y^{\prime }\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime }+y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime \prime }+x y^{\prime \prime }+\left (2 x y-1\right ) y^{\prime }+y^{2}-f \left (x \right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime \prime }+x \left (y-1\right ) y^{\prime \prime }+x {y^{\prime }}^{2}+\left (1-y\right ) y^{\prime } = 0 \] |
✗ |
N/A |
|
|
\[ {}\left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }-\left (3 y^{\prime }+a \right ) {y^{\prime \prime }}^{2} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime } y^{\prime \prime \prime \prime }-y^{\prime \prime } y^{\prime \prime \prime }+{y^{\prime }}^{3} y^{\prime \prime \prime } = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime } \left (f^{\prime \prime \prime }\left (x \right ) y^{\prime }+3 f^{\prime \prime }\left (x \right ) y^{\prime \prime }+3 f^{\prime }\left (x \right ) y^{\prime \prime \prime }+f \left (x \right ) y^{\prime \prime \prime \prime }\right )-y^{\prime \prime } f y^{\prime \prime \prime }+{y^{\prime }}^{3} \left (f^{\prime }\left (x \right ) y^{\prime }+f \left (x \right ) y^{\prime \prime }\right )+2 q \left (x \right ) {y^{\prime }}^{2} \sin \left (y\right )+\left (q \left (x \right ) y^{\prime \prime }-q^{\prime }\left (x \right ) y^{\prime }\right ) \cos \left (y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-f \left (y\right ) = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime } = y^{2}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )} \] |
✗ |
N/A |
|
|
\[ {}y y^{\prime }-y = a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}} \] |
✗ |
N/A |
|
|
\[ {}x y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+c x \left (-c \,x^{2}+x a +b +1\right ) = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} \left (x -a \right )^{2} y^{\prime \prime }+b y = c \,x^{2} \left (x -a \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{{\mathrm e}^{x}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 2 \,{\mathrm e}^{-x}-{\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = x^{2}+\cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \,{\mathrm e}^{2 x} x -\sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \,{\mathrm e}^{x}+x^{3}-x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{2 x}-\cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime } = 3 x^{2}+\sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = {\mathrm e}^{x}+4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{2 x}+1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+x y^{\prime }-y = x \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y = 10 x +\frac {10}{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }-\left (1+x \right ) y^{\prime }+6 y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \cos \left (x \right )-{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y = {\mathrm e}^{x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 x^{3}-x \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime } = x^{2}-3 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (1+\ln \left (x \right )\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = x^{2}-x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sec \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y = {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {1}{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y = x \,{\mathrm e}^{x}+\cos \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = x \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = x^{2}-x -1 \] |
✓ |
✓ |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}\sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }+3 y \sin \left (x \right ) = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }-x y = 2 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\left (2 \,{\mathrm e}^{x}-1\right ) y^{\prime }+{\mathrm e}^{2 x} y = {\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y = \frac {1}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-8 x^{3} y = 4 x^{3} {\mathrm e}^{-x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime } = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}\left (y^{\prime }-x y^{\prime \prime }\right )^{2} = 1+{y^{\prime \prime }}^{2} \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime } = {\mathrm e}^{y} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime \prime }-y^{\prime \prime }-x y^{\prime }+y = -x^{2}+1 \] |
✗ |
N/A |
|
|
\[ {}\left (2+x \right )^{2} y^{\prime \prime \prime }+\left (2+x \right ) y^{\prime \prime }+y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }+4 \left (-1+x \right ) y^{\prime }+2 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 2 \] |
✓ |
✓ |
|
|
\[ {}x \left (2 y+x \right ) y^{\prime \prime }+2 x {y^{\prime }}^{2}+4 \left (x +y\right ) y^{\prime }+2 y+x^{2} = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2} = 0 \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}x^{\prime \prime } = -3 \sqrt {t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime }+t x^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}\frac {x^{\prime }+t x^{\prime \prime }}{t} = -2 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime } = 3 t \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = 3 t^{3}-1 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = 3 \cos \left (t \right )-2 \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = 12 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = t^{2} {\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (7 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = {\mathrm e}^{2 t} \cos \left (t \right )+t^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = t \,{\mathrm e}^{-t} \sin \left (\pi t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = \left (2+t \right ) \sin \left (\pi t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = 4 t +5 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (2 t \right )+t \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = t^{3}+1-4 t \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x = -6+2 \,{\mathrm e}^{2 t} \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+7 x = t \,{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-x^{\prime } = 6+{\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = t^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-3 x^{\prime }-4 x = 2 t^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = 9 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-4 x = \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+2 x = t \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-b x^{\prime }+x = \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-3 x^{\prime }-40 x = 2 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-2 x^{\prime } = 4 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+2 x = \cos \left (\sqrt {2}\, t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x = \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+w^{2} x = \cos \left (\beta t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+3025 x = \cos \left (45 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \tan \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-x = t \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-x = \frac {1}{t} \] |
✓ |
✓ |
|
|
\[ {}t^{2} x^{\prime \prime }-2 x = t^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \frac {1}{t +1} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-2 x^{\prime }+x = \frac {{\mathrm e}^{t}}{2 t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\frac {x^{\prime }}{t} = a \] |
✓ |
✓ |
|
|
\[ {}t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-x = \frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime \prime }+x^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime \prime }+x^{\prime \prime } = 2 \,{\mathrm e}^{t}+3 t^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-2 x^{\prime }+2 x = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x = 1-\operatorname {Heaviside}\left (t -5\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+9 x = \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-2 x = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x = \cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\pi ^{2} x = \pi ^{2} \operatorname {Heaviside}\left (1-t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-4 x = 1-\operatorname {Heaviside}\left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+3 x^{\prime }+2 x = {\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-x = \delta \left (t -5\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \delta \left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = 3 \delta \left (t -2 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x = \frac {\left (t -5\right ) \operatorname {Heaviside}\left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = -8 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2-12 x +6 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+8 y = 4 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 6 \sin \left (2 x \right )+7 \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 10 \sin \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+4 y = \cos \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-4 y = 16 x -12 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+5 y = 2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 5 \,{\mathrm e}^{-2 x} x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }+y^{\prime }-6 y = -18 x^{2}+1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-3 y^{\prime }-10 y = 8 \,{\mathrm e}^{-2 x} x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }+3 y^{\prime }-5 y = 5 \sin \left (2 x \right )+10 x^{2}+3 x +7 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+3 y = 3 x^{3}-8 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 6 \,{\mathrm e}^{-2 x}+3 \,{\mathrm e}^{x}-4 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 4 \,{\mathrm e}^{x}-18 \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 9 \,{\mathrm e}^{2 x}-8 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime } = 2 x^{2}+4 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime } = 3 \,{\mathrm e}^{-x}+6 \,{\mathrm e}^{2 x}-6 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = x \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 3 x^{2} {\mathrm e}^{x}-7 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 12 x^{2}-16 x \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime } = 18 x^{2}+16 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x}-9 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+7 y^{\prime \prime }-5 y^{\prime }+6 y = 5 \sin \left (x \right )-12 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 16 x +20 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 9 \,{\mathrm e}^{2 x} x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 4 x \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = 8 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 27 \,{\mathrm e}^{-6 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 18 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+29 y = 8 \,{\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 8 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \,{\mathrm e}^{2 x} x +6 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 3 x^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 3 x^{2}-4 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 8 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y = 3 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-\sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }-4 y = 8 x^{2}+3-6 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = x^{3}+x +{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x}+{\mathrm e}^{3 x} \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-2 x} \left (\cos \left (x \right )+1\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = x^{4} {\mathrm e}^{x}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = x \,{\mathrm e}^{-3 x} \sin \left (2 x \right )+x^{2} {\mathrm e}^{-2 x} \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = x^{2} {\mathrm e}^{x}+3 \,{\mathrm e}^{2 x} x +5 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = {\mathrm e}^{2 x} x +x^{2} {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-x} x^{2}+3 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-16 y = x^{2} \sin \left (2 x \right )+x^{4} {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\left (6\right )}+2 y^{\left (5\right )}+5 y^{\prime \prime \prime \prime } = x^{3}+{\mathrm e}^{-x} x^{2}+{\mathrm e}^{-x} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = x^{2} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+16 y = x \,{\mathrm e}^{\sqrt {2}\, x} \sin \left (\sqrt {2}\, x \right )+{\mathrm e}^{-\sqrt {2}\, x} \cos \left (\sqrt {2}\, x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = \cos \left (x \right )^{2}-\cosh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = \sin \left (2 x \right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cot \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right )^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sec \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-2 x} \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x} \tan \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 x}}{x^{3}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x} \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right )^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{x}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{{\mathrm e}^{2 x}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \arcsin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \frac {{\mathrm e}^{-x}}{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = x \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-6 x y^{\prime }+10 y = 3 x^{4}+6 x^{3} \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = 1 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = \left (2+x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}\left (-2+x \right ) x y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (-1+x \right ) y = 3 x^{2} \left (-2+x \right )^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right ) \left (1+x \right ) y^{\prime \prime }+2 x y^{\prime }-2 y = \left (2 x +1\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}\sin \left (x \right )^{2} y^{\prime \prime }-2 \sin \left (x \right ) \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y = \sin \left (x \right )^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = x^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 4 x -6 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 2 x \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 4 \sin \left (\ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 y = 4 x -8 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = -6 x^{3}+4 x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 10 x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-6 y = \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-4 x = t^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-4 x^{\prime } = t^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }-2 x = 3 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }-2 x = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+2 x^{\prime }+x = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\omega ^{2} x = \sin \left (\alpha t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\omega ^{2} x = \sin \left (\omega t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+6 x^{\prime }+10 x = {\mathrm e}^{-2 t} \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = {\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x^{\prime }-2 x = 12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x = 289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\omega ^{2} x = \cos \left (\alpha t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\omega ^{2} x = \cos \left (\omega t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime \prime \prime }-4 x^{\prime \prime \prime }+8 x^{\prime \prime }-8 x^{\prime }+4 x = \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime \prime \prime }-5 x^{\prime \prime }+4 x = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-x = \frac {1}{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \cot \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}t^{2} x^{\prime \prime }-2 x = t^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-4 x^{\prime } = \tan \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (\tan \left (x \right )^{2}-1\right ) y^{\prime \prime }-4 \tan \left (x \right )^{3} y^{\prime }+2 y \sec \left (x \right )^{4} = \left (\tan \left (x \right )^{2}-1\right ) \left (1-2 \sin \left (x \right )^{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+10 y = 100 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \sin \left (t \right )-\cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )^{3}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cosh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }-4 x^{\prime }+4 x = {\mathrm e}^{t}+{\mathrm e}^{2 t}+1 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{3} x^{\prime \prime }+1 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-16 y = x^{2}-{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x^{\left (6\right )}-x^{\prime \prime \prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime \prime \prime }-2 x^{\prime \prime }+x = t^{2}-3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2} = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 1-\frac {1}{\sin \left (x \right )} \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+9 x = t \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = \sinh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = x \,{\mathrm e}^{x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 y = 1 \] |
✓ |
✓ |
|
|
\[ {}m x^{\prime \prime } = f \left (x\right ) \] |
✗ |
N/A |
|
|
\[ {}m x^{\prime \prime } = f \left (x^{\prime }\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\left (6\right )}-3 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-y^{\prime \prime \prime } = x \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime \prime \prime }+2 x^{\prime \prime }+x = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 2 \cos \left (\ln \left (1+x \right )\right ) \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}x^{\prime \prime \prime \prime }+x = t^{3} \] |
✓ |
✓ |
|
|
\[ {}{y^{\prime \prime }}^{3}+y^{\prime \prime }+1 = x \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+10 x^{\prime }+25 x = 2^{t}+t \,{\mathrm e}^{-5 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\left (6\right )}-y = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\left (6\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime } = x +{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (3 x \right ) \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+x y = \sin \left (x \right ) \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+y y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime } = 2 x^{2}+3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y y^{\prime \prime \prime \prime } = 1 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime }+x y = \cosh \left (x \right ) \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime }+x y = \cosh \left (x \right ) \] |
✗ |
N/A |
|
|
\[ {}2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y = 1 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-y = \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = y+x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+x y^{\prime \prime }-y^{2} = \sin \left (x \right ) \] |
✗ |
N/A |
|
|
\[ {}\sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime } = 1 \] |
✗ |
N/A |
|
|
\[ {}y y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}{y^{\prime \prime \prime }}^{2}+\sqrt {y} = \sin \left (x \right ) \] |
✗ |
N/A |
|
|
\[ {}\left (x -3\right ) y^{\prime \prime }+\ln \left (x \right ) y = x^{2} \] |
✗ |
N/A |
|
|
\[ {}x y^{\prime \prime }+2 x^{2} y^{\prime }+y \sin \left (x \right ) = \sinh \left (x \right ) \] |
✗ |
N/A |
|
|
\[ {}\sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+7 y = 1 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+x^{2} y = \tan \left (x \right ) \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+\frac {k x}{y^{4}} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+2 x^{2} y^{\prime }+4 x y = 2 x \] |
✓ |
✓ |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 1-2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\cot \left (x \right ) y^{\prime }-\csc \left (x \right )^{2} y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x \ln \left (x \right ) y^{\prime \prime }+2 y^{\prime }-\frac {y}{x} = 1 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1 = 0 \] |
✗ |
N/A |
|
|
\[ {}\frac {x y^{\prime \prime }}{y+1}+\frac {y y^{\prime }-x {y^{\prime }}^{2}+y^{\prime }}{\left (y+1\right )^{2}} = x \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime } \sin \left (x \right )+\left (\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y\right ) y^{\prime } = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (\cos \left (y\right )-y \sin \left (y\right )\right ) y^{\prime \prime }-{y^{\prime }}^{2} \left (2 \sin \left (y\right )+y \cos \left (y\right )\right ) = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\frac {\left (x^{2}-x \right ) y^{\prime \prime }}{x}+\frac {\left (1+3 x \right ) y^{\prime }}{x}+\frac {y}{x} = 3 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {\left (-1+x \right ) y^{\prime }}{x}+\frac {y}{x^{3}} = \frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+\left (5+2 x \right ) y^{\prime }+\left (4 x +8\right ) y = {\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+8 y^{\prime \prime }+16 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+13 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+13 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = 9 t \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+16 y^{\prime }+17 y = 17 t -1 \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+5 y^{\prime }+4 y = 3 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t^{2} {\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-3 y^{\prime }+17 y = 17 t -1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 2+t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+20 y = \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = t^{2} \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }+y^{\prime }-y = 4 \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }+5 y^{\prime }-2 y = 7 \,{\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-1+t \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 39 \operatorname {Heaviside}\left (t \right )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (t -4\right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (t -4\right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+5 y = 25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-1+t \right )+\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 \pi ^{2} y = 3 \delta \left (t -\frac {1}{3}\right )-\delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 3 \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+29 y = 5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 1-\delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y = 8 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 4 t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y = -t^{2}+2 t -10 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-16 y = 32 \operatorname {Heaviside}\left (t \right )-32 \operatorname {Heaviside}\left (t -\pi \right ) \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = t^{7} \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-6 t y^{\prime }+\sin \left (2 t \right ) y = \ln \left (t \right ) \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+\frac {y}{t} = t \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+t y^{\prime }-y \ln \left (t \right ) = \cos \left (2 t \right ) \] |
✗ |
N/A |
|
|
\[ {}t^{3} y^{\prime \prime }-2 t y^{\prime }+y = t^{4} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-7 y = 4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 5 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }+5 y^{\prime }-2 y = 3 t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime } = 2 y^{\prime \prime }-4 y^{\prime }+\sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = x^{\frac {3}{2}} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 2 \sec \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = f \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-\nu ^{2}+x^{2}\right ) y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 k y^{\prime }+k^{2} y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {1}{2 y^{\prime }} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime \prime } = 2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {a}{y^{3}} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = x^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\tan \left (x \right ) y^{\prime } = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}{y^{\prime \prime }}^{2}+{y^{\prime }}^{2} = a^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {1}{2 y^{\prime }} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime } = {y^{\prime \prime }}^{2} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2} = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = x \] |
✓ |
✓ |
|
|
\[ {}s^{\prime \prime }-a^{2} s = t +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 8 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 5 x +2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+5 y = {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 6 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 2-6 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+3 y = {\mathrm e}^{-x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 2 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 2 x +3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-a^{4} y = 5 a^{4} {\mathrm e}^{x a} \sin \left (x a \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 8 \cos \left (x a \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+n^{2} y = h \sin \left (r x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \frac {1}{\cos \left (2 x \right )^{\frac {3}{2}}} \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = {\mathrm e}^{2 x} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime } = \left (2 \cos \left (x\right )-1\right ) \sin \left (x\right ) \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }-2 y^{\prime }+4 y = x \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime \prime }+x y^{\prime } = 4 \] |
✓ |
✓ |
|
|
\[ {}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2} \] |
✓ |
✓ |
|
|
\[ {}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2} \] |
✓ |
✓ |
|
|
\[ {}\sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}-4\right ) y^{\prime \prime }+\ln \left (x \right ) y = x \,{\mathrm e}^{x} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-4 y = 31 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 27 x +18 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = -3 x -\frac {3}{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 2 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 24 x^{2}-6 x +14+32 \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3+\cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = 6 x -20-120 x^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y = 36 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = \left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y = {\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 2 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 x +4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = 2 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{x}-3 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x \,{\mathrm e}^{x}-3 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = 2+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 2+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+6 y = -2 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = -x^{2}+1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x +\cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 18 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (-1+x \right )^{2} & 1\le x \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \delta \left (x -\pi \right )+\delta \left (x -3 \pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \delta \left (-1+x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = \cos \left (x \right )+2 \delta \left (x -\pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \cos \left (x \right ) \delta \left (x -\pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a^{2} y = \delta \left (x -\pi \right ) f \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \,{\mathrm e}^{-3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 4 \,{\mathrm e}^{-3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 3 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-\frac {t}{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-\frac {t}{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 5 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 10 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+6 y = -8 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y = -3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}y^{\prime \prime }+9 y = 6 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y = -{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = -3 t^{2}+2 t +3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 3 t +2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 3 t +2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = t -\frac {1}{20} t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 4+{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-t}-4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = t +{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 6+t^{2}+{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 5 \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 2 \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = -4 \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 3 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = -\cos \left (5 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+y = \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 3+2 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-t} \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 5 \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = -\cos \left (\frac {t}{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 3 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 2 \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 8 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = {\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 2 \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (t -4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y = 5 \delta \left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = -2 \delta \left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (-1+t \right )-3 \delta \left (t -4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = {\mathrm e}^{-2 t} \sin \left (4 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \frac {1+x}{-1+x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{2} y^{\prime \prime } = 8 x^{2} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+8 y = {\mathrm e}^{-x^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 = \sqrt {x} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime } y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-{y^{\prime }}^{2} = 6 x^{5} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 2 y^{\prime }-6 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime \prime }+2 y^{\prime \prime } = 6 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime } = 2 \sqrt {y^{\prime \prime }} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime } y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = 6 x^{5} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime \prime }+2 y^{\prime \prime } = 6 x \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime } = 6 \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime } y^{\prime \prime } = {y^{\prime }}^{2}-1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }-4 y = x^{3} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime } = 2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }-83 y-25 = 0 \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime } = y \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = \sqrt {x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-20 y = 27 x^{5} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1+x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y = {\mathrm e}^{3 x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 24 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 24 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-8 y = 8 x^{2}-3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-8 y = 8 x^{2}-3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = 36 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -6 \,{\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 7 \,{\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 169 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 10 x +12 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = {\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = {\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 35 \,{\mathrm e}^{5 x}+12 \,{\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 22 x +24 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = x \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 4 x^{2}+2 x +3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 52 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = 30 \,{\mathrm e}^{-4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{\frac {x}{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -5 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 10 \cos \left (2 x \right )+15 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 25 \sin \left (6 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -4 \cos \left (x \right )+7 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -200 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 18 x^{2}+3 x +4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 9 x^{4}-9 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 54 x^{2} {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 6 x \,{\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left (12 x -4\right ) {\mathrm e}^{-5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 39 \,{\mathrm e}^{2 x} x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = -3 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 20 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 3 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 10 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = \left (72 x^{2}-1\right ) {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 4 x \,{\mathrm e}^{6 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{-5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 24 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 8 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{-x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 100 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 10 x^{2}+4 x +8 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 6 \cos \left (x \right )-3 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 6 \cos \left (2 x \right )-3 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{-x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{2 x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{-8 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{4 x} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{2 x} \sin \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = x^{3} \sin \left (4 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{2} {\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{4} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 12 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 10 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 32 \,{\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 32 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 6 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 x \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 3 x \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 3 x \,{\mathrm e}^{x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 5 x^{5} {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right )+3 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 5 \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 20 \sinh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = \frac {5}{x^{3}} \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {50}{x^{3}} \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 85 \cos \left (2 \ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 y = 15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y = 4 x^{3} \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = \frac {10}{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 6 x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 64 \ln \left (x \right ) x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 3 \sqrt {x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cot \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \csc \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 6 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \left (24 x^{2}+2\right ) {\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = \sqrt {x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 12 x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \ln \left (x \right ) \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}x^{2} y^{\prime \prime }-2 y = \frac {1}{-2+x} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = x^{3} {\mathrm e}^{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1+x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = \frac {10}{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 12 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime } = 30 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = {\mathrm e}^{-x^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = \tan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-81 y = \sinh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 x y^{\prime }+9 y = 12 x \sin \left (x^{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}2 x y^{\prime \prime }+y^{\prime } = \sqrt {x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime } = 8 \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-7 y^{\prime }+3 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y^{\prime }+14 y = 98 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 25 \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y^{\prime }+14 y = 576 \,{\mathrm e}^{-x} x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 81 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 3 \sqrt {x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-12 y^{\prime }+36 y = 3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+36 y = 6 \sec \left (6 x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 18 \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }-2 y = 10 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 2 \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 6 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = \frac {1}{x^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = x \,{\mathrm e}^{\frac {3 x}{2}} \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime }+8 y^{\prime }-3 y = 123 x \sin \left (3 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+8 y = {\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\left (6\right )}-64 y = {\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1+x \right )^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = t^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 20 \,{\mathrm e}^{4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = t^{2} {\mathrm e}^{4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 7 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-27 y = {\mathrm e}^{-3 t} \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime }+y^{\prime }+t y = 0 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+9 y = 27 t^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+7 y = 165 \,{\mathrm e}^{4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t^{2} {\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = {\mathrm e}^{t} \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+40 y = 122 \,{\mathrm e}^{-3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = 24 \,{\mathrm e}^{-3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = {\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -10\right ) \] |
✓ |
✓ |
|
|
\[
{}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 |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \delta \left (t -3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \delta \left (-1+t \right )-\delta \left (t -4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t \right )+\delta \left (t -\pi \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = -2 \delta \left (t -\frac {\pi }{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = \delta \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = \delta \left (t -2\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-16 y = \delta \left (t -10\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t \right ) \] |
✓ |
✗ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right ) \] |
✓ |
✗ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (t -4\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right ) \] |
✓ |
✗ |
|
|
\[ {}y^{\prime \prime \prime }+9 y^{\prime } = \delta \left (-1+t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-16 y = \delta \left (t \right ) \] |
✓ |
✗ |
|
|
\[ {}y^{\prime \prime }+x y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+5 y^{\prime }+y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}x {y^{\prime \prime }}^{2}+2 y = 2 x \] |
✗ |
N/A |
|
|
\[ {}x^{\prime \prime }+2 \sin \left (x\right ) = \sin \left (2 t \right ) \] |
✗ |
N/A |
|
|
\[ {}x^{\prime \prime }+x = t \cos \left (t \right )-\cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = 2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = t \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}} = \frac {1}{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 8 \,{\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = -{\mathrm e}^{-9 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 2 \,{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 2 t -4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 3-4 t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 4 \cos \left (t \right )-\sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \cos \left (2 t \right )+t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 3 t \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 3 t^{4}-2 t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = -1 \] |
✓ |
✓ |
|
|
\[ {}5 y^{\prime \prime }+y^{\prime }-4 y = -3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 32 t \] |
✓ |
✓ |
|
|
\[ {}16 y^{\prime \prime }-8 y^{\prime }-15 y = 75 t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+26 y = -338 t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = -32 t^{2} \] |
✓ |
✓ |
|
|
\[ {}8 y^{\prime \prime }+6 y^{\prime }+y = 5 t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = -256 t^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 52 \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 25 \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = 54 t \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = -78 \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = -32 t^{2} \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-20 y = -2 \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }-5 y = -648 t^{2} {\mathrm e}^{5 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = -2 t^{3} {\mathrm e}^{4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = t^{2}+{\mathrm e}^{t}+\sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 18 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = 32 t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = -2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 3 t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = 4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = t \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = -1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = -{\mathrm e}^{3 t}-2 t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = -3 t -4 t^{2} {\mathrm e}^{2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 2 t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = {\mathrm e}^{-3 t}-{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 \pi ^{2} y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 2 t -2 \pi & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 10 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = f \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+9 x = \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+37 y = \cos \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y^{\prime } = t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = {\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = 2 \cos \left (4 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 2 t \,{\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\frac {y}{4} = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = \csc \left (4 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = \cot \left (4 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+50 y = {\mathrm e}^{-t} \csc \left (7 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = {\mathrm e}^{-3 t} \left (\sec \left (4 t \right )+\csc \left (4 t \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+26 y = {\mathrm e}^{t} \left (\sec \left (5 t \right )+\csc \left (5 t \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+12 y^{\prime }+37 y = {\mathrm e}^{-6 t} \csc \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+34 y = {\mathrm e}^{3 t} \tan \left (5 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+34 y = {\mathrm e}^{5 t} \cot \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-12 y^{\prime }+37 y = {\mathrm e}^{6 t} \sec \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 t} \sec \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-25 y = \frac {1}{1-{\mathrm e}^{5 t}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 2 \sinh \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 t}}{t^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{4}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 t}}{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \ln \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{t}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{-2 t} \sqrt {-t^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \sqrt {-t^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 t} \ln \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 t} \arctan \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \tan \left (3 t \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sec \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \tan \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \tan \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = \tan \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \tan \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sec \left (3 t \right ) \tan \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sec \left (2 t \right ) \tan \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \frac {\csc \left (3 t \right )}{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sec \left (2 t \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-16 y = 16 t \,{\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (t \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sec \left (2 t \right )+\tan \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \csc \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 65 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = \ln \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+4 y = t \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 2 \ln \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = f \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y = t^{3}+2 t \] |
✗ |
N/A |
|
|
\[ {}t y^{\prime \prime }+2 y^{\prime }+t y = -t \] |
✓ |
✓ |
|
|
\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{\frac {3}{2}} \] |
✗ |
N/A |
|
|
\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{\frac {3}{2}} \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}t^{2} \left (\ln \left (t \right )-1\right ) y^{\prime \prime }-t y^{\prime }+y = -\frac {3 \left (1+\ln \left (t \right )\right )}{4 \sqrt {t}} \] |
✓ |
✓ |
|
|
\[ {}\left (\sin \left (t \right )-t \cos \left (t \right )\right ) y^{\prime \prime }-t \sin \left (t \right ) y^{\prime }+\sin \left (t \right ) y = t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-16 y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}-y^{\prime \prime \prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+9 y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+9 y^{\prime \prime } = 9 \,{\mathrm e}^{3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+10 y^{\prime \prime }+34 y^{\prime }+40 y = t \,{\mathrm e}^{-4 t}+2 \,{\mathrm e}^{-3 t} \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \,{\mathrm e}^{-3 t}-t \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-24 y^{\prime }+36 y = 108 t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }-14 y^{\prime }-104 y = -111 \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-10 y^{\prime \prime \prime }+38 y^{\prime \prime }-64 y^{\prime }+40 y = 153 \,{\mathrm e}^{-t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+4 y^{\prime } = \tan \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+4 y^{\prime } = \sec \left (2 t \right ) \tan \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = \sec \left (2 t \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = \tan \left (2 t \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+9 y^{\prime } = \sec \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime } = -\sec \left (t \right ) \tan \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+4 y^{\prime } = \sec \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime } = -\frac {1}{t^{2}}-\frac {2}{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = \frac {{\mathrm e}^{t}}{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }-11 y^{\prime }+30 y = {\mathrm e}^{4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-10 y^{\prime }-24 y = {\mathrm e}^{-3 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-13 y^{\prime }+12 y = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\left (6\right )}+y^{\prime \prime \prime \prime } = -24 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime } = \tan \left (t \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime } = 3 t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime } = \sec \left (t \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime } = \sec \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime } = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime } = t \] |
✓ |
✓ |
|
|
\[ {}t^{2} \ln \left (t \right ) y^{\prime \prime \prime }-t y^{\prime \prime }+y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}\left (t^{2}+t \right ) y^{\prime \prime \prime }+\left (-t^{2}+2\right ) y^{\prime \prime }-\left (2+t \right ) y^{\prime } = -t -2 \] |
✓ |
✓ |
|
|
\[ {}2 t^{3} y^{\prime \prime \prime }+t^{2} y^{\prime \prime }+t y^{\prime }-y = -3 t^{2} \] |
✓ |
✓ |
|
|
\[ {}t y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime } = \frac {45}{8 t^{\frac {7}{2}}} \] |
✗ |
N/A |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \frac {1}{x^{5}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = \frac {1}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = \frac {1}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 2 x \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 8 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+36 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-11 x y^{\prime }+16 y = \frac {1}{x^{3}} \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+70 x y^{\prime }+80 y = \frac {1}{x^{13}} \] |
✓ |
✓ |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}4 x^{2} y^{\prime \prime }+y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}9 x^{2} y^{\prime \prime }+27 x y^{\prime }+10 y = \frac {1}{x} \] |
✓ |
✓ |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 x y^{\prime } = -8 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+x y^{\prime } = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+x y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-\cos \left (x \right ) y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = -t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime } = 5 t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = -3 \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = \frac {1}{{\mathrm e}^{2 t}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = -4 \,{\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 3 \,{\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y^{\prime }+20 y = -2 t \,{\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 3 t^{2} {\mathrm e}^{-4 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }+5 y = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-12 y^{\prime }-16 y = {\mathrm e}^{4 t}-{\mathrm e}^{-2 t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+18 y^{\prime \prime }+30 y^{\prime }+25 y = {\mathrm e}^{-t} \cos \left (2 t \right )+{\mathrm e}^{-2 t} \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }+20 y^{\prime }+25 y = t^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y = t \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sin \left (3 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \tan \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \csc \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \ln \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \ln \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 8 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}t \left (y^{\prime \prime } y+{y^{\prime }}^{2}\right )+y^{\prime } y = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+13 x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 1-t & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \cos \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \cos \left (\frac {9 t}{10}\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = \cos \left (\frac {7 t}{10}\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+\frac {x^{\prime }}{10}+x = 3 \cos \left (2 t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+16 x = t \sin \left (t \right ) \] |
✓ |
✓ |
|
|
\[ {}x^{\prime \prime }+x = {\mathrm e}^{t} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \cos \left (x \right )+2 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime \prime } = 2 \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \] |
✓ |
✓ |
|
|
\[ {}{y^{\prime }}^{2}+y y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime } = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime } = x +\cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } \left (2+x \right )^{5} = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 2 x \ln \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime } = y^{\prime }+x^{2} \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime } = \frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \sqrt {1-{y^{\prime }}^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime } = \sqrt {y^{\prime }+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+2 = 0 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \] |
✓ |
✓ |
|
|
\[ {}y y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
✓ |
✓ |
|
|
\[ {}2 y y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{3} y^{\prime \prime } = -1 \] |
✓ |
✗ |
|
|
\[ {}y^{\prime \prime } = {\mathrm e}^{2 y} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime } = \left (-1+x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime } = {\mathrm e}^{-7 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \left (1-x \right ) {\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 x} \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }-3 y^{\prime } = x \,{\mathrm e}^{\frac {3 x}{4}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = x \,{\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+25 y = \cos \left (5 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (x \right )-\cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+16 y = \sin \left (4 x +\alpha \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )+\cos \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )-\cos \left (2 x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = {\mathrm e}^{-3 x} \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+k^{2} y = k \sin \left (k x +\alpha \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+k^{2} y = k \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y = x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime } = 2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime } = 3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y^{\prime } = 2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime } = 3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime } = 4 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = x \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = x \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y = a \sin \left (n x +\alpha \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 n^{2} y^{\prime \prime }+n^{4} y = \cos \left (n x +\alpha \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = -2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = -2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 9 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}5 y^{\prime \prime \prime }-7 y^{\prime \prime } = 3 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime } = -6 \] |
✓ |
✓ |
|
|
\[ {}3 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime } = 2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime } = 8 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 k y^{\prime }+k^{2} y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 8 \,{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 9 \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}7 y^{\prime \prime }-y^{\prime } = 14 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 3 x \,{\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 10 \left (1-x \right ) {\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 1+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \left (x^{2}+x \right ) {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-2 y = 8 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 4 x \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 m y^{\prime }+m^{2} y = \sin \left (n x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+a^{2} y = 2 \cos \left (m x \right )+3 \sin \left (m x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 4 \left (\cos \left (x \right )+\sin \left (x \right )\right ) {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 10 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}4 y^{\prime \prime }+8 y^{\prime } = x \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = x^{2} {\mathrm e}^{4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \left (x^{2}+x \right ) {\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = x^{2}+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = x^{3} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime } = x^{2}+x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = x^{2} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \cos \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \left (\sin \left (x \right )+2 \cos \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{x}+{\mathrm e}^{-2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = x +{\mathrm e}^{-4 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = x +\sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = \left (\sin \left (x \right )+1\right ) {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime } = 1+{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
|
|||
|
\[ {}y^{\prime \prime \prime }+4 y^{\prime } = {\mathrm e}^{2 x}+\sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 x \right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 2 \cos \left (4 x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 4 x -2 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 18 x -10 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2+{\mathrm e}^{x} \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \left (5 x +4\right ) {\mathrm e}^{x}+{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}2 y^{\prime \prime }-3 y^{\prime }-2 y = 5 \,{\mathrm e}^{x} \cosh \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = x \sin \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = x \,{\mathrm e}^{x}+\frac {\cos \left (x \right )}{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime } = {\mathrm e}^{x}+3 \sin \left (2 x \right )+1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 10 \sin \left (x \right )+17 \sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x^{2}-{\mathrm e}^{-x}+{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 2 x +{\mathrm e}^{-x}-2 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = {\mathrm e}^{x}+4 \sin \left (2 x \right )+2 \cos \left (x \right )^{2}-1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 6 x \,{\mathrm e}^{-x} \left (1-{\mathrm e}^{-x}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \cos \left (2 x \right )^{2}+\sin \left (\frac {x}{2}\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 1+8 \cos \left (x \right )+{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (\frac {x}{2}\right )^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x} \left (1-2 \sin \left (x \right )^{2}\right )+10 x +1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 4 x +\sin \left (x \right )+\sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 1+2 \cos \left (x \right )+\cos \left (2 x \right )-\sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y+1 = \sin \left (x \right )+x +x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 18 \,{\mathrm e}^{-3 x}+8 \sin \left (x \right )+6 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+1 = 3 \sin \left (2 x \right )+\cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = 2 x +{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \sin \left (2 x \right ) \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime } = 4 x +3 \sin \left (x \right )+\cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime } = {\mathrm e}^{2 x} x +\sin \left (x \right )+x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}-y^{\prime \prime \prime \prime } = x \,{\mathrm e}^{x}-1 \] |
✓ |
✓ |
|
|
\[ {}y^{\left (5\right )}-y^{\prime \prime \prime } = x +2 \,{\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2-2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 9 x^{2}-12 x +2 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = 36 \,{\mathrm e}^{3 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \left (12 x -7\right ) {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 2 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = 4 x \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 2 x^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 16 \,{\mathrm e}^{-x}+9 x -6 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = -5 \,{\mathrm e}^{-x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 4 \,{\mathrm e}^{x} \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime } = -2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y = 8 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }-y = 2 x \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime \prime }-y = 8 \,{\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = \sin \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \cos \left (2 x \right )+\sin \left (2 x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = 1 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y = -2 \cos \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-x} \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 8 \,{\mathrm e}^{x}+9 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-5 y = 1 \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right ) \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right ) \] |
✗ |
N/A |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right ) \] |
✗ |
N/A |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime \prime }-12 y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}\left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } = 0 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = x \left (6-\ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 y = \sin \left (\ln \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = -\frac {16 \ln \left (x \right )}{x} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y = x^{2}-2 x +2 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m} \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 \ln \left (x \right )^{2}+12 x \] |
✓ |
✓ |
|
|
\[ {}\left (1+x \right )^{3} y^{\prime \prime }+3 \left (1+x \right )^{2} y^{\prime }+\left (1+x \right ) y = 6 \ln \left (1+x \right ) \] |
✓ |
✓ |
|
|
\[ {}\left (-2+x \right )^{2} y^{\prime \prime }-3 \left (-2+x \right ) y^{\prime }+4 y = x \] |
✓ |
✓ |
|
|
\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (1+x \right ) y^{\prime }+6 y = 6 \] |
✓ |
✓ |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = 1 \] |
✓ |
✓ |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 5 x^{4} \] |
✓ |
✓ |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = \left (-1+x \right )^{2} {\mathrm e}^{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+{\mathrm e}^{-2 x} y = {\mathrm e}^{-3 x} \] |
✓ |
✓ |
|
|
\[ {}\left (x^{4}-x^{3}\right ) y^{\prime \prime }+\left (2 x^{3}-2 x^{2}-x \right ) y^{\prime }-y = \frac {\left (-1+x \right )^{2}}{x} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y = {\mathrm e}^{2 x} x -1 \] |
✓ |
✓ |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y = x^{2} \left (2 x -3\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \frac {1}{1+{\mathrm e}^{x}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \frac {1}{\cos \left (x \right )^{3}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \frac {{\mathrm e}^{-x}}{\sin \left (x \right )} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y = \frac {2}{\sin \left (x \right )^{3}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime } = \frac {-1+x}{x^{3}} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime } = 4 x^{3} {\mathrm e}^{x^{2}} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime } = 1 \] |
✓ |
✓ |
|
|
\[ {}x \ln \left (x \right ) y^{\prime \prime }-y^{\prime } = \ln \left (x \right )^{2} \] |
✓ |
✓ |
|
|
\[ {}x y^{\prime \prime }+\left (2 x -1\right ) y^{\prime } = -4 x^{2} \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\tan \left (x \right ) y^{\prime } = \cos \left (x \right ) \cot \left (x \right ) \] |
✓ |
✓ |
|
|
\[ {}4 x y^{\prime \prime }+2 y^{\prime }+y = 1 \] |
✗ |
N/A |
|
|
\[ {}4 x y^{\prime \prime }+2 y^{\prime }+y = \frac {6+x}{x^{2}} \] |
✗ |
N/A |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {1}{x^{2}+1} \] |
✓ |
✓ |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (-1+x \right )^{2} {\mathrm e}^{x} \] |
✗ |
N/A |
|
|
\[ {}2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y = \frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}} \] |
✗ |
N/A |
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\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y = 4 \,{\mathrm e}^{x} \] |
✗ |
N/A |
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\[ {}x^{3} \left (-1+\ln \left (x \right )\right ) y^{\prime \prime }-x^{2} y^{\prime }+x y = 2 \ln \left (x \right ) \] |
✗ |
N/A |
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\[ {}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-2 \left (1-x \right ) y = 2 x -2 \] |
✗ |
N/A |
|
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\[ {}x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x = 0 \] |
✗ |
N/A |
|
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\[ {}y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+\alpha ^{2} y = 1 \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }+y = 1 \] |
✓ |
✓ |
|
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\[ {}x y^{\prime \prime }+y \sin \left (x \right ) = x \] |
✓ |
✓ |
|
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\[ {}y^{\prime \prime }-x y^{\prime }+y = 1 \] |
✓ |
✓ |
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\[ {}y^{\prime \prime }+4 y = \cos \left (x \right )^{2} \] |
✓ |
✓ |
|
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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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\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = \arcsin \left (\sin \left (x \right )\right ) \] |
✓ |
✓ |
|
|
\[ {}y^{\prime \prime }+9 y = \sin \left (x \right )^{3} \] |
✓ |
✓ |
|
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\[ {}x^{\prime \prime } = 1 \] |
✓ |
✓ |
|
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\[ {}x^{\prime \prime } = \cos \left (t \right ) \] |
✓ |
✓ |
|
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\[ {}x^{\prime \prime }-x^{\prime } = 1 \] |
✓ |
✓ |
|
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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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