|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 4 y
\] |
[_quadrature] |
✓ |
0.566 |
|
|
\[
{}2 y^{\prime }+3 y = 0
\] |
[_quadrature] |
✓ |
0.566 |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
0.588 |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
0.575 |
|
|
\[
{}\left (-2+x \right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.606 |
|
|
\[
{}\left (2 x -1\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
0.614 |
|
|
\[
{}2 \left (x +1\right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.633 |
|
|
\[
{}\left (x -1\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
0.671 |
|
|
\[
{}2 \left (x -1\right ) y^{\prime } = 3 y
\] |
[_separable] |
✓ |
0.612 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.527 |
|
|
\[
{}y^{\prime \prime } = 4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.564 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.562 |
|
|
\[
{}y^{\prime \prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.359 |
|
|
\[
{}x y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.494 |
|
|
\[
{}2 x y^{\prime } = y
\] |
[_separable] |
✓ |
0.496 |
|
|
\[
{}x^{2} y^{\prime }+y = 0
\] |
[_separable] |
✗ |
0.098 |
|
|
\[
{}x^{3} y^{\prime } = 2 y
\] |
[_separable] |
✗ |
0.107 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.582 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.602 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.599 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.614 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.927 |
|
|
\[
{}y^{\prime \prime } = y^{\prime }+y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.631 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.232 |
|
|
\[
{}y^{\prime \prime \prime } = y
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.137 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.629 |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.635 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.542 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.647 |
|
|
\[
{}\left (x^{2}-3\right ) y^{\prime \prime }+2 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.596 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.549 |
|
|
\[
{}\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.636 |
|
|
\[
{}\left (-x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.637 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.635 |
|
|
\[
{}3 y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.587 |
|
|
\[
{}5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.599 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.600 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.595 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.497 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.493 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.559 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.506 |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.562 |
|
|
\[
{}\left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.679 |
|
|
\[
{}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.607 |
|
|
\[
{}\left (4 x^{2}+16 x +17\right ) y^{\prime \prime } = 8 y
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.660 |
|
|
\[
{}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.650 |
|
|
\[
{}y^{\prime \prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.548 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.674 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.592 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.650 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.617 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{-x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.780 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.879 |
|
|
\[
{}x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
1.610 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+2 \alpha y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.648 |
|
|
\[
{}x y^{\prime \prime }+\left (-x^{3}+x \right ) y^{\prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.086 |
|
|
\[
{}x y^{\prime \prime }+x^{2} y^{\prime }+\left ({\mathrm e}^{x}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.889 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } \cos \left (x \right )+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.195 |
|
|
\[
{}3 x^{3} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.130 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+2 y^{\prime }+3 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.422 |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.898 |
|
|
\[
{}x^{2} y^{\prime \prime }+6 \sin \left (x \right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.004 |
|
|
\[
{}\left (2 x^{3}+6 x^{2}\right ) y^{\prime \prime }+21 x y^{\prime }+9 \left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.063 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.658 |
|
|
\[
{}\left (1-x \right )^{2} y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.689 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.641 |
|
|
\[
{}\left (-2+x \right )^{3} y^{\prime \prime }+3 \left (-2+x \right )^{2} y^{\prime }+x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.724 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+\left (-2+x \right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.718 |
|
|
\[
{}\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x^{2}+9\right ) y^{\prime }+\left (x^{2}+4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.821 |
|
|
\[
{}\left (-2+x \right )^{2} y^{\prime \prime }-\left (x^{2}-4\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.727 |
|
|
\[
{}x^{3} \left (1-x \right ) y^{\prime \prime }+\left (2+3 x \right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.141 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.908 |
|
|
\[
{}2 x y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.868 |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.880 |
|
|
\[
{}3 x y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.889 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.903 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (-2 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.913 |
|
|
\[
{}6 x^{2} y^{\prime \prime }+7 x y^{\prime }-\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.865 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+2 x y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.774 |
|
|
\[
{}2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.925 |
|
|
\[
{}2 x y^{\prime \prime }+\left (-2 x^{2}+1\right ) y^{\prime }-4 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.831 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+9 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.823 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-4 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.812 |
|
|
\[
{}4 x y^{\prime \prime }+8 y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.817 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.778 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-4 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.888 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.045 |
|
|
\[
{}\left (5 x^{3}+2 x^{2}\right ) y^{\prime \prime }+\left (-x^{2}+3 x \right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.152 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.980 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
0.179 |
|
|
\[
{}x^{3} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
0.125 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.897 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.266 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.924 |
|
|
\[
{}x \left (x -1\right ) \left (x +1\right )^{2} y^{\prime \prime }+2 x \left (x -3\right ) \left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.599 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) x \right ) y^{\prime }-\alpha \beta y = 0
\] |
[_Jacobi] |
✓ |
1.239 |
|
|
\[
{}x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.877 |
|
|
\[
{}x y^{\prime \prime }+\left (5-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.939 |
|
|
\[
{}x y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.953 |
|