|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+x^{2} y = x^{2}+x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.337 |
|
|
\[
{}2 \left (x^{3}+x^{2}\right ) y^{\prime \prime }-\left (-3 x^{2}+x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.635 |
|
|
\[
{}4 x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.638 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.627 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.418 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.509 |
|
|
\[
{}x y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.198 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.578 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.721 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }-y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.783 |
|
|
\[
{}2 x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.686 |
|
|
\[
{}x^{3} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.611 |
|
|
\[
{}z^{\prime \prime }+t z^{\prime }+\left (t^{2}-\frac {1}{9}\right ) z = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.357 |
|
|
\[
{}x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.788 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+x y^{\prime }\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.684 |
|
|
\[
{}x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.028 |
|
|
\[
{}x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.032 |
|
|
\[
{}2 x^{2} \left (2-x \right ) y^{\prime \prime }-\left (-x +4\right ) x y^{\prime }+\left (3-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.803 |
|
|
\[
{}\left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.477 |
|
|
\[
{}x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.471 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 \left (x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.829 |
|
|
\[
{}x y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime }+b x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.523 |
|
|
\[
{}\left (-1+x \right ) \left (-2+x \right ) y^{\prime \prime }+\left (4 x -6\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.434 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.324 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.332 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.371 |
|
|
\[
{}y^{\prime \prime } = \left (-1+x \right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.323 |
|
|
\[
{}x \left (x +2\right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.560 |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.038 |
|
|
\[
{}y^{\prime \prime }+\left (-1+{\mathrm e}^{x}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.444 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.295 |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.476 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }-y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.836 |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.225 |
|
|
\[
{}x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.717 |
|
|
\[
{}x y^{\prime \prime }+\left (\frac {1}{2}-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.656 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.494 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {9}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.493 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {25}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.496 |
|
|
\[
{}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.313 |
|
|
\[
{}y^{\prime }+x y = \cos \left (x \right )
\] |
[_linear] |
✓ |
0.477 |
|
|
\[
{}y^{\prime }+x y = \frac {1}{x^{3}}
\] |
[_linear] |
✓ |
1.273 |
|
|
\[
{}x^{3} y^{\prime \prime }+y = \frac {1}{x^{4}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.074 |
|
|
\[
{}x y^{\prime \prime }-2 y^{\prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
1.335 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = \cos \left (x \right )
\] |
[_linear] |
✗ |
0.163 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.454 |
|
|
\[
{}y^{\prime \prime }+4 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.233 |
|
|
\[
{}y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.372 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.246 |
|
|
\[
{}y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
0.350 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.522 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.220 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.356 |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.398 |
|
|
\[
{}y^{\prime \prime }+2 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.246 |
|
|
\[
{}y^{\prime \prime }-x y = \frac {1}{1-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.374 |
|
|
\[
{}x^{2} y^{\prime \prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.490 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.621 |
|
|
\[
{}x^{2} y^{\prime \prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.483 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.426 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.546 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.569 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.218 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.120 |
|
|
\[
{}x y^{\prime \prime }+x^{3} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.265 |
|
|
\[
{}x y^{\prime \prime }+x y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.360 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.300 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.362 |
|
|
\[
{}x^{3} y^{\prime \prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.088 |
|
|
\[
{}x y^{\prime \prime }+x^{5} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.236 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.342 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }-y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.749 |
|
|
\[
{}x^{2} y^{\prime \prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.484 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x -\frac {3}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.230 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.457 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }-4 x y^{\prime }+5 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
1.022 |
|
|
\[
{}x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y = 0
\] |
[NONE] |
✗ |
0.033 |
|
|
\[
{}t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.040 |
|
|
\[
{}u^{\prime \prime }+u^{\prime }+u = \cos \left (r +u\right )
\] |
[NONE] |
✗ |
0.396 |
|
|
\[
{}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.958 |
|
|
\[
{}R^{\prime \prime } = -\frac {k}{R^{2}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
66.076 |
|
|
\[
{}x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.937 |
|
|
\[
{}\sin \left (y^{\prime }\right ) = x +y
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.645 |
|
|
\[
{}\sin \left (x^{\prime }\right )+y^{3} x = \sin \left (y \right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
25.205 |
|
|
\[
{}y^{2}-1+x y^{\prime } = 0
\] |
[_separable] |
✓ |
1.862 |
|
|
\[
{}2 y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
1.640 |
|
|
\[
{}y^{\prime }+20 y = 24
\] |
[_quadrature] |
✓ |
1.664 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.590 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.915 |
|
|
\[
{}\left (y-x \right ) y^{\prime } = y-x
\] |
[_quadrature] |
✓ |
1.017 |
|
|
\[
{}y^{\prime } = 25+y^{2}
\] |
[_quadrature] |
✓ |
9.631 |
|
|
\[
{}y^{\prime } = 2 x y^{2}
\] |
[_separable] |
✓ |
2.152 |
|
|
\[
{}2 y^{\prime } = y^{3} \cos \left (x \right )
\] |
[_separable] |
✓ |
2.945 |
|
|
\[
{}x^{\prime } = \left (x-1\right ) \left (1-2 x\right )
\] |
[_quadrature] |
✓ |
1.827 |
|
|
\[
{}2 x y+\left (x^{2}-y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.366 |
|
|
\[
{}p^{\prime } = p \left (1-p\right )
\] |
[_quadrature] |
✓ |
2.217 |
|
|
\[
{}y^{\prime }+4 x y = 8 x^{3}
\] |
[_linear] |
✓ |
1.613 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.959 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 12 x^{2}
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.299 |
|
|
\[
{}x y^{\prime }-3 x y = 1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.143 |
|