|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{2}+2 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.723 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \frac {x -1}{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.696 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.176 |
|
|
\[
{}y^{\prime \prime }+9 y = -3 \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.056 |
|
|
\[
{}y^{\prime }+y = \cos \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.110 |
|
|
\[
{}y^{\prime \prime } = -3 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
5.127 |
|
|
\[
{}y^{\prime \prime }+\sin \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.807 |
|
|
\[
{}y^{\prime } = 2 y x
\] |
[_separable] |
✓ |
0.581 |
|
|
\[
{}y^{\prime } = 2 y x
\] |
[_separable] |
✓ |
1.017 |
|
|
\[
{}y^{\prime }+y = 1
\] |
[_quadrature] |
✓ |
0.281 |
|
|
\[
{}y^{\prime }+y = 1
\] |
[_quadrature] |
✓ |
0.350 |
|
|
\[
{}y^{\prime }-y = 2
\] |
[_quadrature] |
✓ |
0.482 |
|
|
\[
{}y^{\prime }-y = 2
\] |
[_quadrature] |
✓ |
0.314 |
|
|
\[
{}y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
0.257 |
|
|
\[
{}y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
0.454 |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.448 |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.435 |
|
|
\[
{}y^{\prime }-y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.498 |
|
|
\[
{}y^{\prime }-y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.879 |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
0.408 |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
1.100 |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✗ |
0.078 |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✓ |
1.194 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
0.458 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
1.088 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x
\] |
[_linear] |
✓ |
1.056 |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {-x^{2}+1}}
\] |
[_quadrature] |
✓ |
0.319 |
|
|
\[
{}y^{\prime } = 1+y
\] |
[_quadrature] |
✓ |
0.273 |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.525 |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.003 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.610 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.711 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x -y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.649 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-x^{2} y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.788 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.652 |
|
|
\[
{}y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.629 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.599 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.573 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.537 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.579 |
|
|
\[
{}y^{\prime \prime }+\left (p +\frac {1}{2}-\frac {x^{2}}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.676 |
|
|
\[
{}y^{\prime \prime }+y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.494 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +p^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.847 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 p y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.667 |
|
|
\[
{}x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.116 |
|
|
\[
{}x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.568 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✗ |
0.152 |
|
|
\[
{}\left (3 x +1\right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.613 |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.840 |
|
|
\[
{}x y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.773 |
|
|
\[
{}x^{2} y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.339 |
|
|
\[
{}x^{3} y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.905 |
|
|
\[
{}x^{4} y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.128 |
|
|
\[
{}x^{3} y^{\prime \prime }+\left (\cos \left (2 x \right )-1\right ) y^{\prime }+2 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.992 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.061 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +4 y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.286 |
|
|
\[
{}x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.819 |
|
|
\[
{}4 x y^{\prime \prime }+3 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.024 |
|
|
\[
{}2 x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.959 |
|
|
\[
{}2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.056 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.091 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y = 0
\] |
[_Lienard] |
✓ |
0.703 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
0.111 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
0.161 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (4 x +4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.881 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.047 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
0.812 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.057 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.750 |
|
|
\[
{}\left (x -1\right )^{2} y^{\prime \prime }-3 \left (x -1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.800 |
|
|
\[
{}3 \left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.865 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.218 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.903 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
1.156 |
|
|
\[
{}\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.907 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.124 |
|
|
\[
{}\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.084 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +p^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.523 |
|
|
\[
{}\left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }+\frac {y^{\prime }}{2}+y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.298 |
|
|
\[
{}y^{\prime \prime }+2 y x = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.531 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.602 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{3}-x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.406 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.586 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.715 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.588 |
|
|
\[
{}y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.648 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.690 |
|
|
\[
{}\left (x^{2}+1\right ) x^{2} y^{\prime \prime }-y^{\prime } x +\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.940 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.846 |
|
|
\[
{}x y^{\prime \prime }-4 y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
0.937 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x^{2} y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.970 |
|
|
\[
{}2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.099 |
|
|
\[
{}x y^{\prime \prime }-\left (x -1\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
0.863 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.943 |
|
|
\[
{}x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.804 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+y x = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.006 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (x -1\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.006 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-y x = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.006 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.006 |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.843 |
|