|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
74.799 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.131 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.133 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x +1
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.188 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x^{2}+x +1
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.237 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x^{3}+x^{2}+x +1
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.306 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.468 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \cos \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.479 |
|
|
\[
{}y^{\prime \prime }+y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.600 |
|
|
\[
{}y^{\prime \prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.078 |
|
|
\[
{}y^{\prime \prime }+y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.293 |
|
|
\[
{}y^{\prime \prime }+y = x^{2}+x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.334 |
|
|
\[
{}y^{\prime \prime }+y = x^{3}+x^{2}+x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.604 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.307 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.399 |
|
|
\[
{}y {y^{\prime \prime }}^{2}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
12.101 |
|
|
\[
{}y {y^{\prime \prime }}^{2}+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.400 |
|
|
\[
{}y^{2} {y^{\prime \prime }}^{2}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
5.201 |
|
|
\[
{}y {y^{\prime \prime }}^{4}+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
61.293 |
|
|
\[
{}y^{3} {y^{\prime \prime }}^{2}+y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
5.738 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.543 |
|
|
\[
{}y {y^{\prime \prime }}^{3}+y^{3} y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
84.460 |
|
|
\[
{}y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
23.197 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.307 |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.417 |
|
|
\[
{}y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y^{2} {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.135 |
|
|
\[
{}y^{\prime \prime }+\left (\sin \left (x \right )+2 x \right ) y^{\prime }+\cos \left (y\right ) y {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.608 |
|
|
\[
{}y^{\prime \prime } y^{\prime }+y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.789 |
|
|
\[
{}y^{\prime \prime } y^{\prime }+y^{n} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.249 |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{4}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
160.084 |
|
|
\[
{}y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (3+y^{2}\right ) {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.144 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.318 |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.188 |
|
|
\[
{}3 y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\sin \left (y\right ) {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.634 |
|
|
\[
{}10 y^{\prime \prime }+x^{2} y^{\prime }+\frac {3 {y^{\prime }}^{2}}{y} = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.331 |
|
|
\[
{}10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.994 |
|
|
\[
{}y^{\prime \prime }-\frac {2 y}{x^{2}} = x \,{\mathrm e}^{-\sqrt {x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.249 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.813 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.372 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -c^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.290 |
|
|
\[
{}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.576 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y = 2 x^{3}-x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.150 |
|
|
\[
{}y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+4 y \csc \left (x \right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.989 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 4 \cos \left (\ln \left (x +1\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
1.393 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.915 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 8 x^{3} \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
30.741 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.900 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 y \cos \left (x \right )^{3} = 2 \cos \left (x \right )^{5}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.168 |
|
|
\[
{}y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x} = 4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.205 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+x y = x^{m +1}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.178 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.454 |
|
|
\[
{}\cos \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y = 0
\] |
[_Lienard] |
✓ |
3.464 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.479 |
|
|
\[
{}y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y = x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
51.928 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-3\right ) y = {\mathrm e}^{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.281 |
|
|
\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = {\mathrm e}^{x^{2}} \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
17.495 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 \left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.398 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.629 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-y+y^{\prime } x \right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.149 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.327 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
1.653 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 \cos \left (x \right )
\] |
[_linear] |
✓ |
1.873 |
|
|
\[
{}2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.497 |
|
|
\[
{}y^{\prime } = x -y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.060 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y = x \,{\mathrm e}^{x}+3 \,{\mathrm e}^{-2 x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.208 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.309 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y = 0
\] |
[_Bessel] |
✓ |
0.875 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y = 0
\] |
[_Bessel] |
✓ |
1.394 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.256 |
|
|
\[
{}y^{\prime \prime \prime }-x y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.050 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
2.031 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+y \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.398 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.266 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.281 |
|
|
\[
{}\left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.426 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.255 |
|
|
\[
{}3 y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.289 |
|
|
\[
{}5 y^{\prime \prime }-2 y^{\prime } x +10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.325 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.372 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.344 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.289 |
|
|
\[
{}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.375 |
|
|
\[
{}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.271 |
|
|
\[
{}t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.425 |
|
|
\[
{}t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.133 |
|
|
\[
{}t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
0.283 |
|
|
\[
{}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.293 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.212 |
|
|
\[
{}t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
0.291 |
|
|
\[
{}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.281 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.278 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.311 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.293 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime } x +3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.304 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.268 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.299 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.278 |
|
|
\[
{}\left (-x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.125 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.153 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.291 |
|