|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = \sin \left (x \right )+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.948 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (\cos \left (x \right )-1\right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.087 |
|
|
\[
{}\left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.845 |
|
|
\[
{}\left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.974 |
|
|
\[
{}\left (x +1\right ) \left (3 x -1\right ) y^{\prime \prime }+\cos \left (x \right ) y^{\prime }-3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.171 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.733 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x -x y = x^{2}+2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.978 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.916 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 y^{\prime } x -x y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.732 |
|
|
\[
{}y^{\prime \prime }+\left (x -6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.565 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.905 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.033 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.033 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{3}+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.098 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{3} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.978 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{3} \cos \left (x \right )+\sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.135 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.799 |
|
|
\[
{}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.994 |
|
|
\[
{}x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.913 |
|
|
\[
{}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.874 |
|
|
\[
{}{y^{\prime }}^{2}+y^{2} = \sec \left (x \right )^{4}
\] |
[‘y=_G(x,y’)‘] |
✓ |
33.454 |
|
|
\[
{}\left (y-2 y^{\prime } x \right )^{2} = {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✗ |
257.822 |
|
|
\[
{}x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.605 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.719 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.844 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.723 |
|
|
\[
{}x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.748 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.185 |
|
|
\[
{}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.912 |
|
|
\[
{}2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.912 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.047 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 y^{\prime } x -x y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.963 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 y^{\prime } x -x y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.884 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 y^{\prime } x -x y = \cos \left (x \right ) \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.991 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 y^{\prime } x -x y = x^{3}+x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.996 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+2 y^{\prime } x -x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.852 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.814 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.724 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.797 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.187 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}+6 x \right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.885 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-8\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.203 |
|
|
\[
{}x^{2} y^{\prime \prime }-9 y^{\prime } x +25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.641 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.868 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.865 |
|
|
\[
{}x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.856 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.710 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.620 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.717 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.079 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.720 |
|
|
\[
{}y^{\prime } = y \left (1-y^{2}\right )
\] |
[_quadrature] |
✓ |
3.124 |
|
|
\[
{}\frac {x y^{\prime \prime }}{1-x}+y = \frac {1}{1-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.628 |
|
|
\[
{}\frac {x y^{\prime \prime }}{1-x}+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.940 |
|
|
\[
{}\frac {x y^{\prime \prime }}{1-x}+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.812 |
|
|
\[
{}\frac {x y^{\prime \prime }}{-x^{2}+1}+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.312 |
|
|
\[
{}y^{\prime \prime } = \left (x^{2}+3\right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.168 |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.509 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+2 t +1 \\ y^{\prime }=5 x+y+3 t -1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.747 |
|
|
\[
{}y^{\prime \prime }+20 y^{\prime }+500 y = 100000 \cos \left (100 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
82.342 |
|
|
\[
{}y^{\prime \prime } \sin \left (2 x \right )^{2}+y^{\prime } \sin \left (4 x \right )-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
4.484 |
|
|
\[
{}y^{\prime \prime } = A y^{{2}/{3}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.808 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.802 |
|
|
\[
{}y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.942 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.702 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.976 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 6 x^{3} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.039 |
|
|
\[
{}y^{\prime }+y = \frac {1}{x}
\] |
[[_linear, ‘class A‘]] |
✗ |
0.224 |
|
|
\[
{}y^{\prime }+y = \frac {1}{x^{2}}
\] |
[[_linear, ‘class A‘]] |
✗ |
0.243 |
|
|
\[
{}y^{\prime } x +y = 0
\] |
[_separable] |
✓ |
0.503 |
|
|
\[
{}y^{\prime } = \frac {1}{x}
\] |
[_quadrature] |
✗ |
0.137 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{x}
\] |
[[_2nd_order, _quadrature]] |
✗ |
0.058 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \frac {1}{x}
\] |
[[_2nd_order, _missing_y]] |
✗ |
0.072 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.066 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \frac {1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.065 |
|
|
\[
{}h^{2}+\frac {2 a h}{\sqrt {1+{h^{\prime }}^{2}}} = b^{2}
\] |
[_quadrature] |
✓ |
18.652 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-24 y = 16-\left (x +2\right ) {\mathrm e}^{4 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.000 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.344 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{a \cos \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.033 |
|
|
\[
{}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.417 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.864 |
|
|
\[
{}x^{2} y^{\prime }+{\mathrm e}^{-y} = 0
\] |
[_separable] |
✓ |
1.071 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{y} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
13.977 |
|
|
\[
{}y^{\prime } = \frac {x y+3 x -2 y+6}{x y-3 x -2 y+6}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.287 |
|
|
\[
{}y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.666 |
|
|
\[
{}y^{\prime } = a
\] |
[_quadrature] |
✓ |
0.337 |
|
|
\[
{}y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.449 |
|
|
\[
{}y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.751 |
|
|
\[
{}y^{\prime } = a x
\] |
[_quadrature] |
✓ |
0.166 |
|
|
\[
{}y^{\prime } = y a x
\] |
[_separable] |
✓ |
0.862 |
|
|
\[
{}y^{\prime } = a x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.673 |
|
|
\[
{}y^{\prime } = a x +b y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.790 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
1.310 |
|
|
\[
{}y^{\prime } = b y
\] |
[_quadrature] |
✓ |
0.675 |
|
|
\[
{}y^{\prime } = a x +b y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.013 |
|
|
\[
{}c y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.674 |
|
|
\[
{}c y^{\prime } = a
\] |
[_quadrature] |
✓ |
0.349 |
|
|
\[
{}c y^{\prime } = a x
\] |
[_quadrature] |
✓ |
0.214 |
|
|
\[
{}c y^{\prime } = a x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.730 |
|
|
\[
{}c y^{\prime } = a x +b y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.781 |
|