|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+p \left (p +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.739 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = x^{2}+x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.508 |
|
|
\[
{}2 \left (x^{3}+x^{2}\right ) y^{\prime \prime }-\left (-3 x^{2}+x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.874 |
|
|
\[
{}4 x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.828 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.850 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.658 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.757 |
|
|
\[
{}x y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.184 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.738 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.919 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }-y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.008 |
|
|
\[
{}2 x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.867 |
|
|
\[
{}x^{3} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.845 |
|
|
\[
{}z^{\prime \prime }+t z^{\prime }+\left (t^{2}-\frac {1}{9}\right ) z = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.574 |
|
|
\[
{}x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.967 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+x y^{\prime }\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.918 |
|
|
\[
{}x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.006 |
|
|
\[
{}x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.006 |
|
|
\[
{}2 \left (2-x \right ) x^{2} y^{\prime \prime }-\left (4-x \right ) x y^{\prime }+\left (3-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.041 |
|
|
\[
{}\left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.439 |
|
|
\[
{}x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.722 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 \left (x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.999 |
|
|
\[
{}x y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime }+b x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.767 |
|
|
\[
{}\left (x -1\right ) \left (-2+x \right ) y^{\prime \prime }+\left (4 x -6\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.648 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.503 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.502 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.608 |
|
|
\[
{}y^{\prime \prime } = \left (x -1\right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.503 |
|
|
\[
{}x \left (x +2\right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.811 |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.140 |
|
|
\[
{}y^{\prime \prime }+\left ({\mathrm e}^{x}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.623 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.242 |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.722 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }-y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.045 |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.458 |
|
|
\[
{}x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.910 |
|
|
\[
{}x y^{\prime \prime }+\left (\frac {1}{2}-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.834 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.799 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {9}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.740 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {25}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.678 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.486 |
|
|
\[
{}y^{\prime }+x y = \cos \left (x \right )
\] |
[_linear] |
✓ |
0.610 |
|
|
\[
{}y^{\prime }+x y = \frac {1}{x^{3}}
\] |
[_linear] |
✓ |
1.216 |
|
|
\[
{}x^{3} y^{\prime \prime }+y = \frac {1}{x^{4}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.098 |
|
|
\[
{}x y^{\prime \prime }-2 y^{\prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
1.282 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = \cos \left (x \right )
\] |
[_linear] |
✗ |
0.401 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.343 |
|
|
\[
{}y^{\prime \prime }+4 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.464 |
|
|
\[
{}y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.576 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.461 |
|
|
\[
{}y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
0.500 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.674 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.465 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.586 |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.573 |
|
|
\[
{}y^{\prime \prime }+2 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.473 |
|
|
\[
{}y^{\prime \prime }-x y = \frac {1}{1-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.552 |
|
|
\[
{}x^{2} y^{\prime \prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.740 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.862 |
|
|
\[
{}x^{2} y^{\prime \prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.786 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.669 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.764 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.756 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.245 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.162 |
|
|
\[
{}x y^{\prime \prime }+x^{3} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.234 |
|
|
\[
{}x y^{\prime \prime }+x y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.364 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.472 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.312 |
|
|
\[
{}x^{3} y^{\prime \prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.116 |
|
|
\[
{}x y^{\prime \prime }+x^{5} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.187 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.421 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }-y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.967 |
|
|
\[
{}x^{2} y^{\prime \prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.720 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x -\frac {3}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.250 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.642 |
|
|
\[
{}\left (x^{2}-25\right ) y^{\prime \prime }+2 x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.608 |
|
|
\[
{}\left (x^{2}-25\right ) y^{\prime \prime }+2 x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.726 |
|
|
\[
{}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.691 |
|
|
\[
{}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.705 |
|
|
\[
{}y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.451 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.461 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+y = 0
\] |
[_Lienard] |
✓ |
0.512 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+2 y = 0
\] |
[_Hermite] |
✓ |
0.485 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.567 |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.567 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.518 |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.516 |
|
|
\[
{}y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.557 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.567 |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.608 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.578 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.503 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }-\left (2-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.611 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.510 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.574 |
|
|
\[
{}y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.690 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.744 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.503 |
|
|
\[
{}x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
0.121 |
|