|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+\left (\tan \left (x \right )-2 \cot \left (x \right )\right ) y^{\prime }+2 \cot \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.373 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.405 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -y = 1
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.384 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -3 y = 5 x^{4}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.365 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = \left (x -1\right )^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.427 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+{\mathrm e}^{-2 x} y = {\mathrm e}^{-3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.560 |
|
|
\[
{}\left (x^{4}-x^{3}\right ) y^{\prime \prime }+\left (2 x^{3}-2 x^{2}-x \right ) y^{\prime }-y = \frac {\left (x -1\right )^{2}}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.421 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y = x \,{\mathrm e}^{2 x}-1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.647 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y = x^{2} \left (2 x -3\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.413 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.033 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \frac {1}{1+{\mathrm e}^{x}}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.473 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\cos \left (x \right )^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.618 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.754 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.159 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \frac {{\mathrm e}^{-x}}{\sin \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.063 |
|
|
\[
{}y^{\prime \prime }+y = \frac {2}{\sin \left (x \right )^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.622 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.952 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = \frac {x -1}{x^{3}}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.267 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime } = 4 x^{3} {\mathrm e}^{x^{2}}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.074 |
|
|
\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime } = 1
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.619 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime \prime }-y^{\prime } = \ln \left (x \right )^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.965 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x -1\right ) y^{\prime } = -4 x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.082 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime } = \cos \left (x \right ) \cot \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.612 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.302 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = \frac {6+x}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.359 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x = \frac {1}{x^{2}+1}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.546 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = \left (x -1\right )^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.684 |
|
|
\[
{}2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y = \frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.770 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y = 4 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.017 |
|
|
\[
{}x^{3} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x^{2} y^{\prime }+y x = 2 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.683 |
|
|
\[
{}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-2 \left (1-x \right ) y = 2 x -2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.053 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.566 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+6 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.510 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.765 |
|
|
\[
{}x^{\prime \prime }+{x^{\prime }}^{2}+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.862 |
|
|
\[
{}x^{\prime \prime }-2 {x^{\prime }}^{2}+x^{\prime }-2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.456 |
|
|
\[
{}x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.566 |
|
|
\[
{}x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.749 |
|
|
\[
{}x^{\prime \prime }+x {x^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.427 |
|
|
\[
{}x^{\prime \prime }+\left (x+2\right ) x^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.553 |
|
|
\[
{}x^{\prime \prime }-x^{\prime }+x-x^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.484 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.570 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.475 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.942 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.316 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.893 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.648 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.813 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.169 |
|
|
\[
{}y^{\prime \prime }+\alpha y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.651 |
|
|
\[
{}y^{\prime \prime }+\alpha ^{2} y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
7.727 |
|
|
\[
{}y^{\prime \prime }+y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.737 |
|
|
\[
{}y^{\prime \prime }+\lambda ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.707 |
|
|
\[
{}y^{\prime \prime }+\lambda ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.589 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.132 |
|
|
\[
{}y^{\prime \prime \prime \prime }-\lambda ^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.155 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.804 |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }+4 x y^{\prime \prime \prime }+2 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.197 |
|
|
\[
{}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.211 |
|
|
\[
{}y^{\prime } = 1-y x
\] |
[_linear] |
✓ |
0.535 |
|
|
\[
{}y^{\prime } = \frac {-x +y}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.234 |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
0.658 |
|
|
\[
{}y^{\prime \prime }+y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.448 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } \sin \left (x \right ) = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.678 |
|
|
\[
{}x y^{\prime \prime }+y \sin \left (x \right ) = x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.918 |
|
|
\[
{}\ln \left (x \right ) y^{\prime \prime }-y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.377 |
|
|
\[
{}y^{\prime \prime \prime }+x \sin \left (y\right ) = 0
\] |
[NONE] |
✗ |
0.011 |
|
|
\[
{}y^{\prime }-2 y x = 0
\] |
[_separable] |
✓ |
0.516 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.482 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.477 |
|
|
\[
{}y^{\prime \prime }-\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.484 |
|
|
\[
{}y^{\prime \prime } = x^{2} y-y^{\prime }
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.522 |
|
|
\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.687 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{y}+y x
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.308 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.866 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-n y = 0
\] |
[_separable] |
✓ |
0.521 |
|
|
\[
{}9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
[_Jacobi] |
✓ |
0.846 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x^{2}-\frac {1}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.976 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.477 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {y}{9} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.897 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.882 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +4 \left (x^{4}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.076 |
|
|
\[
{}x y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{4} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.272 |
|
|
\[
{}y^{\prime \prime }+\frac {5 y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
0.857 |
|
|
\[
{}y^{\prime \prime }+\frac {3 y^{\prime }}{x}+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.903 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.636 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = \pi ^{2}-x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.031 |
|
|
\[
{}y^{\prime \prime }-4 y = \cos \left (\pi x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.466 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = \arcsin \left (\sin \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.909 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.908 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 t x_{1}^{2} \\ x_{2}^{\prime }=\frac {x_{2}+t}{t} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.053 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }={\mathrm e}^{t -x_{1}} \\ x_{2}^{\prime }=2 \,{\mathrm e}^{x_{1}} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.054 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=\frac {y^{2}}{x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.047 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}^{2}}{x_{2}} \\ x_{2}^{\prime }=x_{2}-x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.048 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {{\mathrm e}^{-x}}{t} \\ y^{\prime }=\frac {x \,{\mathrm e}^{-y}}{t} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.047 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y+t}{x+y} \\ y^{\prime }=\frac {x-t}{x+y} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.048 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {t -y}{-x+y} \\ y^{\prime }=\frac {x-t}{-x+y} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.049 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y+t}{x+y} \\ y^{\prime }=\frac {t +x}{x+y} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.057 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-9 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.337 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+t \\ y^{\prime }=x-t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.374 |
|