These are second order linear ode’s solved using the transformation \(y(x)=v(x) x^n\). Reference: this Number of problems in this table is 444
Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
3.006 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.575 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.498 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.27 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.293 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.148 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.186 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.418 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.455 |
|
|
\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+25 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.691 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.015 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.511 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{4} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.28 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 8 x^{\frac {4}{3}} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.498 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
6.312 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}-1 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.895 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.654 |
|
|
\[ {}t^{2} y^{\prime \prime }+4 t y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.901 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+\frac {5 y}{4} = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.946 |
|
|
\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.383 |
|
|
\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.827 |
|
|
\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.928 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.738 |
|
|
\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.929 |
|
|
\[ {}t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.671 |
|
|
\[ {}t^{2} y^{\prime \prime }+2 t y^{\prime }+\frac {y}{4} = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.64 |
|
|
\[ {}2 t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.15 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.599 |
|
|
\[ {}4 t^{2} y^{\prime \prime }-8 t y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.682 |
|
|
\[ {}t^{2} y^{\prime \prime }+5 t y^{\prime }+13 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.961 |
|
|
\[ {}t^{2} y^{\prime \prime }-t \left (2+t \right ) y^{\prime }+\left (2+t \right ) y = 2 t^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.659 |
|
|
\[ {}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (-1+t \right )^{2} {\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.265 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \ln \left (x \right ) x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.91 |
|
|
\[ {}t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 4 t^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.562 |
|
|
\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.5 |
|
|
\[ {}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (-1+t \right ) {\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.074 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.412 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.379 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.911 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.304 |
|
|
\[ {}4 x^{2} \sin \left (x \right ) y^{\prime \prime }-4 x \left (x \cos \left (x \right )+\sin \left (x \right )\right ) y^{\prime }+\left (2 x \cos \left (x \right )+3 \sin \left (x \right )\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.208 |
|
|
\[ {}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.236 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 2 x^{2}+2 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.238 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{\frac {5}{2}} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.252 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 2 x^{4} \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.786 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y = x^{1+a} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
21.075 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = x^{\frac {3}{2}} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.704 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+2 \left (x +3\right ) y = {\mathrm e}^{x} x^{4} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.997 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 2 \left (-1+x \right )^{2} {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.357 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y = x^{\frac {5}{2}} {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.039 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = -2 x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.133 |
|
|
\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.391 |
|
|
\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
4.299 |
|
|
\[ {}t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.751 |
|
|
\[ {}t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.38 |
|
|
\[ {}t^{2} y^{\prime \prime }-t y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
6.679 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.204 |
|
|
\[ {}t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.766 |
|
|
\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[_Gegenbauer] |
✓ |
✓ |
2.775 |
|
|
\[ {}\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.386 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.682 |
|
|
\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.765 |
|
|
\[ {}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = t^{2}+1 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.929 |
|
|
\[ {}t^{2} y^{\prime \prime }-5 t y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.365 |
|
|
\[ {}t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.343 |
|
|
\[ {}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.304 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.58 |
|
|
\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.729 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.097 |
|
|
\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
4.398 |
|
|
\[ {}t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
3.281 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
6.27 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+16 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.542 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-16 x y^{\prime }+25 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.653 |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.26 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }-18 y = \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.647 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = \ln \left (x^{2}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
9.288 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.391 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 1-x \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
5.723 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 4 x +\sin \left (\ln \left (x \right )\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
30.744 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = \ln \left (x \right ) x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
7.062 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+3 y = \left (-1+x \right ) \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
308.145 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.502 |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.514 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.855 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.283 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 9 x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.592 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.773 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.474 |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.839 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-8 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.826 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \ln \left (x \right ) x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.636 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.77 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.52 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.421 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \cos \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.505 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 9 \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.307 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 8 \ln \left (x \right )^{2} x \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
7.878 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.737 |
|
|
\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+6 y = 4 \,{\mathrm e}^{2 x} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.735 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \frac {x^{2}}{\ln \left (x \right )} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.603 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y = x^{m} \ln \left (x \right )^{k} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
9.447 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.285 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+25 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.694 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.695 |
|
|
\[ {}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = x \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.991 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.967 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} {\mathrm e}^{-x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.137 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.844 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.595 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.545 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.941 |
|
|
\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.026 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.272 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 8 x^{4} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.56 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x -\frac {1}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.462 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 2 x^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.783 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 6 \ln \left (x \right ) x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.773 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 2 x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.932 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.896 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.131 |
|
|
\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.088 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.998 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-2 x \right ) y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.774 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.366 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.588 |
|
|
\[ {}t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N = \ln \left (t \right ) t \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.818 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.651 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.739 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.108 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x +\ln \left (x \right ) x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.908 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = \ln \left (x \right )^{2}-\ln \left (x^{2}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
11.81 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 2 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.546 |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 8 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.884 |
|
|
\[ {}\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right ) = x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
7.556 |
|
|
\[ {}x y^{\prime \prime }-3 y^{\prime }+\frac {3 y}{x} = 2+x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.818 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \frac {-x^{2}+1}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.576 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.218 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.717 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.605 |
|
|
\[ {}x y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.22 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.867 |
|
|
\[ {}x^{3} y^{\prime \prime }+x y^{\prime }-y = \cos \left (\frac {1}{x}\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.593 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }-y = x +\frac {1}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.536 |
|
|
\[ {}x^{2} \left (-1+\ln \left (x \right )\right ) y^{\prime \prime }-x y^{\prime }+y = x \left (1-\ln \left (x \right )\right )^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.549 |
|
|
\[ {}p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u = f \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
7.53 |
|
|
\[ {}y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1} = 0 \] |
1 |
1 |
1 |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.795 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.038 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.88 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.141 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.513 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.326 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.587 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.092 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.629 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (-2-i\right ) x y^{\prime }+3 i y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.288 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 \pi y = x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.379 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.615 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.474 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.625 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
3.393 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.582 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.976 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
3.53 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
3.069 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \left (x^{2}-1\right )^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.388 |
|
|
\[ {}\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y = x \left (1+x \right )^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.458 |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.786 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x \,{\mathrm e}^{-x} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
6.461 |
|
|
\[ {}y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.041 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {2}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
7.598 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
6.595 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.52 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.355 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.201 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.175 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.277 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.403 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.388 |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.615 |
|
|
\[ {}t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.004 |
|
|
\[ {}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.953 |
|
|
\[ {}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.736 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.913 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 2 x^{3}-x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.483 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = x^{1+m} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
7.704 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.481 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.151 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.217 |
|
|
\[ {}y^{\prime \prime }+x^{4} y^{\prime }-x^{3} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.919 |
|
|
\[ {}x y^{\prime \prime }-\left (x^{2}-x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.277 |
|
|
\[ {}x y^{\prime \prime }+\left (f \left (x \right ) x +2\right ) y^{\prime }+f \left (x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.907 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y-x^{2} a = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.91 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+a y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.013 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y-3 x^{3} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.866 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y-x^{5} \ln \left (x \right ) = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.727 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y-x \sin \left (x \right )-\left (x^{2} a +12 a +4\right ) \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
8.401 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y-5 x = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.747 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y-\ln \left (x \right ) x^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.193 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y-x^{4}+x^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.567 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y-\sin \left (x \right ) x^{3} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
7.214 |
|
|
\[ {}x^{2} y^{\prime \prime }+a x y^{\prime }+b y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.714 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (-1+x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.181 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.089 |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.312 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.075 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.867 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.415 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+5 x y^{\prime }-y-\ln \left (x \right ) = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.365 |
|
|
\[ {}\left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime }-2 a^{2} y = 0 \] |
1 |
1 |
1 |
[_Gegenbauer] |
✓ |
✓ |
1.786 |
|
|
\[ {}\left (x^{2} a +b x \right ) y^{\prime \prime }+2 b y^{\prime }-2 a y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.225 |
|
|
\[ {}x^{3} y^{\prime \prime }-x^{2} y^{\prime }+x y-\ln \left (x \right )^{3} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.979 |
|
|
\[ {}x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }+x y-1 = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.872 |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.434 |
|
|
\[ {}y^{\prime \prime } = -\frac {2 \left (-2+x \right ) y^{\prime }}{x \left (-1+x \right )}+\frac {2 \left (1+x \right ) y}{x^{2} \left (-1+x \right )} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.983 |
|
|
\[ {}y^{\prime \prime } = \frac {\left (5 x -4\right ) y^{\prime }}{x \left (-1+x \right )}-\frac {\left (9 x -6\right ) y}{x^{2} \left (-1+x \right )} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.243 |
|
|
\[ {}y^{\prime \prime } = \frac {\left (x -4\right ) y^{\prime }}{2 x \left (-2+x \right )}-\frac {\left (x -3\right ) y}{2 x^{2} \left (-2+x \right )} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.705 |
|
|
\[ {}y^{\prime \prime } = \frac {y^{\prime }}{1+x}-\frac {\left (1+3 x \right ) y}{4 x^{2} \left (1+x \right )} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.703 |
|
|
\[ {}y^{\prime \prime } = \frac {2 \left (x a +2 b \right ) y^{\prime }}{x \left (x a +b \right )}-\frac {\left (2 x a +6 b \right ) y}{\left (x a +b \right ) x^{2}} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.803 |
|
|
\[ {}y^{\prime \prime } = \frac {\left (x^{2}-2\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (x^{2}-2\right ) y}{x^{2} \left (x^{2}-1\right )} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.934 |
|
|
\[ {}y^{\prime \prime } = \frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (a \left (1+a \right )-a \,x^{2} \left (a +3\right )\right ) y}{x^{2} \left (x^{2}-1\right )} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
54.459 |
|
|
\[ {}y^{\prime \prime } = \frac {\left (7 x^{2} a +5\right ) y^{\prime }}{x \left (x^{2} a +1\right )}-\frac {\left (15 x^{2} a +5\right ) y}{x^{2} \left (x^{2} a +1\right )} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.807 |
|
|
\[ {}y^{\prime \prime } = -\frac {y^{\prime }}{x^{4}}+\frac {y}{x^{5}} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.842 |
|
|
\[ {}y^{\prime \prime } = \frac {y^{\prime }}{x \left (-1+\ln \left (x \right )\right )}-\frac {y}{x^{2} \left (-1+\ln \left (x \right )\right )} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.015 |
|
|
\[ {}y^{\prime \prime } = -\frac {x \sin \left (x \right ) y^{\prime }}{x \cos \left (x \right )-\sin \left (x \right )}+\frac {\sin \left (x \right ) y}{x \cos \left (x \right )-\sin \left (x \right )} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
30.27 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (\sin \left (x \right ) x^{2}-2 x \cos \left (x \right )\right ) y^{\prime }}{x^{2} \cos \left (x \right )}-\frac {\left (2 \cos \left (x \right )-x \sin \left (x \right )\right ) y}{x^{2} \cos \left (x \right )} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.051 |
|
|
\[ {}y^{\prime \prime } = -\frac {x y^{\prime }}{f \left (x \right )}+\frac {y}{f \left (x \right )} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.244 |
|
|
\[ {}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }-\left (a \,x^{n -1}+b \,x^{m -1}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.305 |
|
|
\[ {}x y^{\prime \prime }+\left (x^{2} a +b x +c \right ) y^{\prime }+\left (c -1\right ) \left (x a +b \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.681 |
|
|
\[ {}x y^{\prime \prime }+\left (a \,x^{3}+b \right ) y^{\prime }+a \left (b -1\right ) x^{2} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.037 |
|
|
\[ {}x y^{\prime \prime }+\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime }+\left (d -1\right ) \left (x^{2} a +b x +c \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.062 |
|
|
\[ {}x y^{\prime \prime }+\left (a \,x^{n}+2\right ) y^{\prime }+a \,x^{n -1} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.139 |
|
|
\[ {}x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+a \left (b -1\right ) x^{n -1} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.28 |
|
|
\[ {}x y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (c -1\right ) \left (a \,x^{n -1}+b \,x^{m -1}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.428 |
|
|
\[ {}x^{2} y^{\prime \prime }+a x y^{\prime }+b y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.983 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (a \,x^{n}+b \right ) y^{\prime }+b \left (a \,x^{n}-1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.252 |
|
|
\[ {}x^{2} \left (x a +b \right ) y^{\prime \prime }-2 x \left (x a +2 b \right ) y^{\prime }+2 \left (x a +3 b \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.109 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1-x \right )^{2}} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.465 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.58 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.725 |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.987 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.629 |
|
|
\[ {}\left (2 x^{3}-1\right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 x y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.394 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = x^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.515 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = x \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.149 |
|
|
\[ {}x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.261 |
|
|
\[ {}t^{2} x^{\prime \prime }+3 t x^{\prime }+x = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.817 |
|
|
\[ {}t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t} = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
3.08 |
|
|
\[ {}t^{2} x^{\prime \prime }-7 t x^{\prime }+16 x = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.664 |
|
|
\[ {}t^{2} x^{\prime \prime }+3 t x^{\prime }-8 x = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.609 |
|
|
\[ {}t^{2} x^{\prime \prime }-t x^{\prime }+2 x = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.863 |
|
|
\[ {}t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.57 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
3.202 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.202 |
|
|
\[ {}x^{2} y^{\prime \prime }-6 x y^{\prime }+10 y = 3 x^{4}+6 x^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.574 |
|
|
\[ {}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = \left (2+x \right )^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.499 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y = x^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.626 |
|
|
\[ {}x \left (-2+x \right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (-1+x \right ) y = 3 x^{2} \left (-2+x \right )^{2} {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.218 |
|
|
\[ {}\left (2 x +1\right ) \left (1+x \right ) y^{\prime \prime }+2 x y^{\prime }-2 y = \left (2 x +1\right )^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.093 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.478 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.734 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.205 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.919 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.893 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.219 |
|
|
\[ {}3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.035 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.791 |
|
|
\[ {}9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.997 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.097 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 4 x -6 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.065 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.416 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.827 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 2 x \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.044 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 4 \sin \left (\ln \left (x \right )\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
60.531 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.385 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
3.424 |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
4.321 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = -6 x^{3}+4 x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.759 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 10 x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.566 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.29 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
3.365 |
|
|
\[ {}t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
4.056 |
|
|
\[ {}t^{2} x^{\prime \prime }+t x^{\prime }-x = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
4.306 |
|
|
\[ {}x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
26.208 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.656 |
|
|
\[ {}4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.39 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.652 |
|
|
\[ {}3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
4.325 |
|
|
\[ {}t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
6.086 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 2 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.027 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.327 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{1+x}-\frac {\left (2+x \right ) y}{x^{2} \left (1+x \right )} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.566 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = t^{7} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.401 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.733 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.487 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.102 |
|
|
\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.641 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.111 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.969 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.894 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.881 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.908 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.438 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
1 |
0 |
0 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
N/A |
1.063 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.391 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.388 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = -3 x -\frac {3}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.217 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.694 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.521 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.474 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
1 |
0 |
0 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
N/A |
1.587 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.617 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.974 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.55 |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.57 |
|
|
\[ {}x^{2} y^{\prime \prime }-19 x y^{\prime }+100 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.618 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+29 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.948 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.757 |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+29 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.694 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.405 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.679 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-25 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.443 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.579 |
|
|
\[ {}3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.578 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.962 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.485 |
|
|
\[ {}x^{2} y^{\prime \prime }-11 x y^{\prime }+36 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.323 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.377 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.802 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.096 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 10 x +12 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.763 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.341 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.326 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 22 x +24 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.438 |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.988 |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.911 |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.905 |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 4 x^{2}+2 x +3 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.025 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = \frac {5}{x^{3}} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.225 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {50}{x^{3}} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.514 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 85 \cos \left (2 \ln \left (x \right )\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
14.775 |
|
|
\[ {}3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y = 4 x^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.026 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = \frac {10}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.096 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 6 x^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.621 |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 64 \ln \left (x \right ) x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.189 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 3 \sqrt {x} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.726 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = \sqrt {x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.602 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 12 x^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.957 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.657 |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.113 |
|
|
\[ {}x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.189 |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1+x \right )^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.115 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = \frac {10}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.388 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.517 |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.699 |
|
|
\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.795 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.559 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-30 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.296 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.596 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.631 |
|
|
\[ {}9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.632 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 3 \sqrt {x} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.888 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 18 \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.647 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }-2 y = 10 x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.115 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 6 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
6.336 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = \frac {1}{x^{2}+1} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.786 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1+x \right )^{2}} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.776 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.302 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.947 |
|
|
\[ {}x^{2} y^{\prime \prime }-12 x y^{\prime }+42 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.977 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.825 |
|
|
\[ {}t^{2} y^{\prime \prime }-12 t y^{\prime }+42 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
4.648 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
5.391 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-16 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
5.091 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.804 |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.826 |
|
|
\[ {}y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}} = \frac {1}{t} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.964 |
|
|
\[ {}2 t^{2} y^{\prime \prime }-3 t y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.671 |
|
|
\[ {}3 t^{2} y^{\prime \prime }-5 t y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.791 |
|
|
\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }-7 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
4.243 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.97 |
|
|
\[ {}t^{2} y^{\prime \prime }+a t y^{\prime }+b y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.349 |
|
|
\[ {}3 t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.668 |
|
|
\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.598 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = \ln \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
5.294 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+4 y = t \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.547 |
|
|
\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 2 \ln \left (t \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.653 |
|
|
\[ {}t^{2} \left (\ln \left (t \right )-1\right ) y^{\prime \prime }-t y^{\prime }+y = -\frac {3 \left (1+\ln \left (t \right )\right )}{4 \sqrt {t}} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.713 |
|
|
\[ {}\left (\sin \left (t \right )-t \cos \left (t \right )\right ) y^{\prime \prime }-t \sin \left (t \right ) y^{\prime }+\sin \left (t \right ) y = t \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
12.105 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-8 x y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.299 |
|
|
\[ {}3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.232 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.76 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-7 x y^{\prime }+7 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.839 |
|
|
\[ {}9 x^{2} y^{\prime \prime }-9 x y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.359 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-2 x y^{\prime }+20 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.325 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.247 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.172 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.172 |
|
|
\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.17 |
|
|
|
||||||||
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \frac {1}{x^{5}} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.681 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{3} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.467 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = \frac {1}{x^{2}} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
9.394 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = \frac {1}{x^{2}} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
9.445 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 2 x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.912 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.49 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 8 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.369 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+36 y = x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
7.129 |
|
|
\[ {}3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
4.274 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-7 x y^{\prime }+7 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
5.136 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.483 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
4.565 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x^{2}} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.778 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \ln \left (x \right ) \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
8.766 |
|
|
\[ {}9 x^{2} y^{\prime \prime }+27 x y^{\prime }+10 y = \frac {1}{x} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
11.657 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.231 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
4.191 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.844 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
4.118 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = x^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.156 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.634 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.135 |
|
|
\[ {}6 x^{2} y^{\prime \prime }+5 x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.089 |
|
|
\[ {}t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.047 |
|
|
\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.328 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.554 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.039 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
6.456 |
|
|
\[ {}5 x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.429 |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+25 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.359 |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 8 x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.712 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.964 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.899 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.697 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = x \left (6-\ln \left (x \right )\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.521 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = -\frac {16 \ln \left (x \right )}{x} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.35 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y = x^{2}-2 x +2 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.255 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m} \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.67 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 \ln \left (x \right )^{2}+12 x \] |
1 |
1 |
1 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.657 |
|
|
\[ {}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[_Jacobi] |
✓ |
✓ |
1.088 |
|
|
\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (1+x \right ) y^{\prime }+6 y = 6 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.181 |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (-1+x \right )^{2} {\mathrm e}^{x} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.839 |
|
|
\[ {}2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y = \frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}} \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.892 |
|
|
\[ {}x^{3} \left (-1+\ln \left (x \right )\right ) y^{\prime \prime }-x^{2} y^{\prime }+x y = 2 \ln \left (x \right ) \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.788 |
|
|
\[ {}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-2 \left (1-x \right ) y = 2 x -2 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.733 |
|
|
|
||||||||
|
|
||||||||
|
|