|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}{y^{\prime \prime }}^{2} = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.217 |
|
|
\[
{}y^{\prime \prime } = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.115 |
|
|
\[
{}{y^{\prime \prime }}^{2} = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.270 |
|
|
\[
{}{y^{\prime \prime }}^{3} = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.195 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.144 |
|
|
\[
{}{y^{\prime \prime }}^{2}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.610 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.129 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.359 |
|
|
\[
{}{y^{\prime \prime }}^{2}+y^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.630 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.224 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.370 |
|
|
\[
{}{y^{\prime \prime }}^{2}+y^{\prime } = x
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.610 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = x
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.145 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.610 |
|
|
\[
{}{y^{\prime \prime }}^{2}+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.046 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2}+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.803 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
8.855 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
8.822 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
9.977 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{2}+x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
11.613 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{3}+x^{2}+x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
16.318 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
29.197 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
41.556 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.372 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.373 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x +1
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.387 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x^{2}+x +1
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.446 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x^{3}+x^{2}+x +1
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.486 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.648 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \cos \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.629 |
|
|
\[
{}y^{\prime \prime }+y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.908 |
|
|
\[
{}y^{\prime \prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.609 |
|
|
\[
{}y^{\prime \prime }+y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.619 |
|
|
\[
{}y^{\prime \prime }+y = x^{2}+x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.889 |
|
|
\[
{}y^{\prime \prime }+y = x^{3}+x^{2}+x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.040 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.293 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.342 |
|
|
\[
{}y {y^{\prime \prime }}^{2}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
10.099 |
|
|
\[
{}y {y^{\prime \prime }}^{2}+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.198 |
|
|
\[
{}y^{2} {y^{\prime \prime }}^{2}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
5.168 |
|
|
\[
{}y {y^{\prime \prime }}^{4}+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
48.123 |
|
|
\[
{}y^{3} {y^{\prime \prime }}^{2}+y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.342 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.509 |
|
|
\[
{}y {y^{\prime \prime }}^{3}+y^{3} y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.392 |
|
|
\[
{}y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.186 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.286 |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.447 |
|
|
\[
{}y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y^{2} {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.086 |
|
|
\[
{}y^{\prime \prime }+\left (\sin \left (x \right )+2 x \right ) y^{\prime }+\cos \left (y\right ) y {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.251 |
|
|
\[
{}y^{\prime \prime } y^{\prime }+y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.643 |
|
|
\[
{}y^{\prime \prime } y^{\prime }+y^{n} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.056 |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{4}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
154.768 |
|
|
\[
{}y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (3+y^{2}\right ) {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.089 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.284 |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.072 |
|
|
\[
{}3 y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\sin \left (y\right ) {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.572 |
|
|
\[
{}10 y^{\prime \prime }+x^{2} y^{\prime }+\frac {3 {y^{\prime }}^{2}}{y} = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.294 |
|
|
\[
{}10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.365 |
|
|
\[
{}y^{\prime \prime }-\frac {2 y}{x^{2}} = x \,{\mathrm e}^{-\sqrt {x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.184 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.547 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.196 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -c^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.030 |
|
|
\[
{}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.017 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y = 2 x^{3}-x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.784 |
|
|
\[
{}y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+4 y \csc \left (x \right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
7.369 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 4 \cos \left (\ln \left (x +1\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.835 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.755 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 8 x^{3} \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
29.411 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.128 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 y \cos \left (x \right )^{3} = 2 \cos \left (x \right )^{5}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.811 |
|
|
\[
{}y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x} = 4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.773 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+y x = x^{m +1}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.905 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.231 |
|
|
\[
{}\cos \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y = 0
\] |
[_Lienard] |
✓ |
3.667 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.668 |
|
|
\[
{}y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y = x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.742 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-3\right ) y = {\mathrm e}^{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.134 |
|
|
\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = {\mathrm e}^{x^{2}} \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.566 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 \left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.355 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.298 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-y+y^{\prime } x \right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.084 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.234 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
1.418 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 \cos \left (x \right )
\] |
[_linear] |
✓ |
1.621 |
|
|
\[
{}2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.336 |
|
|
\[
{}y^{\prime } = x -y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.022 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y = x \,{\mathrm e}^{x}+3 \,{\mathrm e}^{-2 x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.197 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.331 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y = 0
\] |
[_Bessel] |
✓ |
0.862 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y = 0
\] |
[_Bessel] |
✓ |
1.103 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.014 |
|
|
\[
{}y^{\prime \prime \prime }-y x = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.039 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
0.616 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+y \\ y^{\prime }=-x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.351 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.244 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.244 |
|
|
\[
{}\left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.455 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.227 |
|
|
\[
{}3 y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.265 |
|
|
\[
{}5 y^{\prime \prime }-2 y^{\prime } x +10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.307 |
|