|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.606 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.855 |
|
|
\[
{}y^{\prime \prime }-y y^{\prime } = 2 x
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
7.233 |
|
|
\[
{}y^{\prime }-y^{2}-x -x^{2} = 0
\] |
[_Riccati] |
✓ |
5.803 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -x y-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.755 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -x y-2 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.773 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -x y-3 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.801 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -x y-x^{2}-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.101 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.256 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -x y-x^{4}-6 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.237 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -x y-x^{5}+24 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.211 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -x y-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.845 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -x y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.990 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -x y-x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.167 |
|
|
\[
{}y^{\prime \prime }-a x y^{\prime }-b x y-c x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.938 |
|
|
\[
{}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.877 |
|
|
\[
{}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.925 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.303 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{2} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.198 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.334 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.386 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-x y-x^{2}-2 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.319 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-x y-x^{2}-4 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.334 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{3}+1 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.123 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-x y-x^{3}-x^{2} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.374 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.346 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.331 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.358 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.372 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.340 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{4}+3 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.407 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.167 |
|
|
\[
{}y^{\prime \prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.059 |
|
|
\[
{}y^{\prime \prime }-x y-x^{6}+64 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.656 |
|
|
\[
{}y^{\prime \prime }-x y-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.736 |
|
|
\[
{}y^{\prime \prime }-x y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.521 |
|
|
\[
{}y^{\prime \prime }-x y-x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.573 |
|
|
\[
{}y^{\prime \prime }-x y-x^{6}-x^{3}+42 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.893 |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.784 |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
11.035 |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{4} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.879 |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{4}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.941 |
|
|
\[
{}y^{\prime \prime }-2 x^{2} y-x^{4}+1 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.987 |
|
|
\[
{}y^{\prime \prime }-x^{3} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.694 |
|
|
\[
{}y^{\prime \prime }-x^{3} y-x^{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
36.838 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.093 |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.177 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -x y-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.799 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.200 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{3}-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.122 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.182 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-x y-x^{2}-\frac {1}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
10.594 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.955 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
100.115 |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x y-x^{3}-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.081 |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.039 |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.043 |
|
|
\[
{}y^{\prime \prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3} = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.084 |
|
|
\[
{}y^{\prime \prime }+c y^{\prime }+k y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.427 |
|
|
\[
{}w^{\prime } = -\frac {1}{2}-\frac {\sqrt {1-12 w}}{2}
\] |
[_quadrature] |
✓ |
3.162 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.754 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.737 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.023 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.764 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.737 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.874 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.993 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.893 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.894 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.067 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.968 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime }+y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.596 |
|
|
\[
{}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.764 |
|
|
\[
{}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.745 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.156 |
|
|
\[
{}x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.221 |
|
|
\[
{}x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
4.307 |
|
|
\[
{}5 x^{5} y^{\prime \prime \prime \prime }+4 x^{4} y^{\prime \prime \prime }+x^{2} y^{\prime }+x y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.314 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.949 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = x
\] |
[[_2nd_order, _missing_y]] |
✗ |
397.279 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+x {y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.649 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y {y^{\prime }}^{2} = 0
\] |
[NONE] |
✗ |
0.247 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.670 |
|
|
\[
{}y^{\prime \prime }+\sin \left (y\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.917 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.986 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.940 |
|
|
\[
{}y^{\prime } = 2 x^{2} \sin \left (\frac {y}{x}\right )^{2}+\frac {y}{x}
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
3.394 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 8 \sqrt {x}\, \left (1+\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.642 |
|
|
\[
{}v v^{\prime } = \frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3}
\] |
[_rational, _Bernoulli] |
✓ |
2.102 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.661 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.799 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.735 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.773 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}+x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.854 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.708 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.942 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.897 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.762 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = 1+\sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.943 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.905 |
|