|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime }-4 y = 32 x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.927 |
|
|
\[
{}\left (x^{2}-\frac {2}{y^{3}}\right ) y^{\prime }+2 y x -3 x^{2} = 0
\] |
[_exact, _rational] |
✓ |
2.230 |
|
|
\[
{}y^{\prime }+\frac {3 y}{x} = x^{2}-4 x +3
\] |
[_linear] |
✓ |
1.496 |
|
|
\[
{}2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.179 |
|
|
\[
{}t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}} = 0
\] |
[_separable] |
✓ |
1.227 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }-x^{2} y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.619 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime }-y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.151 |
|
|
\[
{}\left (x^{2}-2\right ) y^{\prime \prime }+2 y^{\prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.547 |
|
|
\[
{}\left (x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }-6 y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.267 |
|
|
\[
{}\left (t^{2}-t -2\right ) x^{\prime \prime }+\left (1+t \right ) x^{\prime }-\left (t -2\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.677 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+\left (x^{2}-2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.627 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.490 |
|
|
\[
{}{\mathrm e}^{x} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+2 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.940 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-y \ln \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.444 |
|
|
\[
{}y^{\prime }+\left (x +2\right ) y = 0
\] |
[_separable] |
✓ |
0.503 |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.431 |
|
|
\[
{}z^{\prime }-x^{2} z = 0
\] |
[_separable] |
✓ |
0.464 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.555 |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.573 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.561 |
|
|
\[
{}w^{\prime \prime }-x^{2} w^{\prime }+w = 0
\] |
[_Lienard] |
✓ |
0.563 |
|
|
\[
{}\left (2 x -3\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.572 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }-3 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.663 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -3 y = 0
\] |
[_Hermite] |
✓ |
0.609 |
|
|
\[
{}\left (x^{2}+x +1\right ) y^{\prime \prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.651 |
|
|
\[
{}\left (x^{2}-5 x +6\right ) y^{\prime \prime }-3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.637 |
|
|
\[
{}y^{\prime \prime }-\tan \left (x \right ) y^{\prime }+y = 0
\] |
[_Lienard] |
✓ |
1.786 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }-y^{\prime } x +2 x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.753 |
|
|
\[
{}y^{\prime }+2 \left (x -1\right ) y = 0
\] |
[_separable] |
✓ |
0.500 |
|
|
\[
{}y^{\prime }-2 y x = 0
\] |
[_separable] |
✓ |
0.549 |
|
|
\[
{}\left (x^{2}-2 x \right ) y^{\prime \prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.596 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.638 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.648 |
|
|
\[
{}y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.632 |
|
|
\[
{}x^{\prime }+\sin \left (t \right ) x = 0
\] |
[_separable] |
✓ |
0.654 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
0.586 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-{\mathrm e}^{x} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.872 |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.711 |
|
|
\[
{}y^{\prime \prime }-{\mathrm e}^{2 x} y^{\prime }+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.204 |
|
|
\[
{}y^{\prime }-y x = \sin \left (x \right )
\] |
[_linear] |
✓ |
0.597 |
|
|
\[
{}w^{\prime }+w x = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
0.543 |
|
|
\[
{}z^{\prime \prime }+x z^{\prime }+z = x^{2}+2 x +1
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.532 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +3 y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.523 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = \cos \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.655 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +2 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.590 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.283 |
|
|
\[
{}y^{\prime \prime }-y \sin \left (x \right ) = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.703 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.704 |
|
|
\[
{}x^{\prime \prime }-\omega ^{2} x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.136 |
|
|
\[
{}x^{\prime \prime \prime }-x^{\prime \prime }+x^{\prime }-x = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}x^{\prime \prime }+42 x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.282 |
|
|
\[
{}x^{\prime \prime \prime \prime }+x = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.070 |
|
|
\[
{}x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x = F \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.763 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.260 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.477 |
|
|
\[
{}y^{\prime \prime }+16 y = 16 \cos \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.196 |
|
|
\[
{}y^{\prime \prime }-y = \cosh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.274 |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.899 |
|
|
\[
{}x^{2} y^{\prime }+2 y x -x +1 = 0
\] |
[_linear] |
✓ |
1.180 |
|
|
\[
{}y^{\prime }+y = \left (x +1\right )^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.127 |
|
|
\[
{}x^{2} y^{\prime }+2 y x = \sinh \left (x \right )
\] |
[_linear] |
✓ |
1.382 |
|
|
\[
{}y^{\prime }+\frac {y}{1-x}+2 x -x^{2} = 0
\] |
[_linear] |
✓ |
0.952 |
|
|
\[
{}y^{\prime }+\frac {y}{1-x}+x -x^{2} = 0
\] |
[_linear] |
✓ |
0.899 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = y x +1
\] |
[_linear] |
✓ |
2.014 |
|
|
\[
{}y^{\prime }+y x = x y^{2}
\] |
[_separable] |
✓ |
1.787 |
|
|
\[
{}3 y^{\prime } x +y+x^{2} y^{4} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.910 |
|
|
\[
{}x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.883 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-2 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.065 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.962 |
|
|
\[
{}x y^{\prime \prime }+\frac {y^{\prime }}{2}+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.268 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.043 |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.140 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.996 |
|
|
\[
{}x \left (x -1\right )^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.907 |
|
|
\[
{}y^{\prime }-\frac {2 y}{x}-x^{2} = 0
\] |
[_linear] |
✓ |
1.173 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x}-x^{3} = 0
\] |
[_linear] |
✓ |
1.208 |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+m y = 0
\] |
[_Laguerre] |
✗ |
0.510 |
|
|
\[
{}y^{\prime } x = x^{2}+2 x -3
\] |
[_quadrature] |
✓ |
0.307 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
1.920 |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.929 |
|
|
\[
{}-y+y^{\prime } x = x^{2}
\] |
[_linear] |
✓ |
1.010 |
|
|
\[
{}x^{2} y^{\prime } = x^{3} \sin \left (3 x \right )+4
\] |
[_quadrature] |
✓ |
0.487 |
|
|
\[
{}x \cos \left (y\right ) y^{\prime }-\sin \left (y\right ) = 0
\] |
[_separable] |
✓ |
3.465 |
|
|
\[
{}\left (x^{3}+x y^{2}\right ) y^{\prime } = 2 y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
73.737 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 y x = x
\] |
[_separable] |
✓ |
1.122 |
|
|
\[
{}y^{\prime }+y \tanh \left (x \right ) = 2 \sinh \left (x \right )
\] |
[_linear] |
✓ |
1.620 |
|
|
\[
{}y^{\prime } x -2 y = x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.516 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.521 |
|
|
\[
{}y^{\prime } x +3 y = x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.579 |
|
|
\[
{}x \left (y-3\right ) y^{\prime } = 4 y
\] |
[_separable] |
✓ |
1.592 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime } = x^{2} y
\] |
[_separable] |
✓ |
1.913 |
|
|
\[
{}x^{3}+\left (1+y\right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.491 |
|
|
\[
{}\cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.444 |
|
|
\[
{}x^{2} \left (1+y\right )+y^{2} \left (x -1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.312 |
|
|
\[
{}\left (2 y-x \right ) y^{\prime } = y+2 x
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.141 |
|
|
\[
{}y x +y^{2}+\left (x^{2}-y x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.175 |
|
|
\[
{}x^{3}+y^{3} = 3 x y^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
9.180 |
|
|
\[
{}y-3 x +\left (4 y+3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.763 |
|
|
\[
{}\left (x^{3}+3 x y^{2}\right ) y^{\prime } = y^{3}+3 x^{2} y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
46.126 |
|