|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.812 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.307 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.113 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.070 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.450 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-2-i\right ) x y^{\prime }+3 i y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.384 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-4 \pi y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.671 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.806 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+x^{6} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.361 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime }+3 x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.138 |
|
|
\[
{}x y^{\prime \prime }+4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.205 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.774 |
|
|
\[
{}\left (x^{2}+x -2\right )^{2} y^{\prime \prime }+3 \left (x +2\right ) y^{\prime }+\left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.171 |
|
|
\[
{}x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.661 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.715 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (4 x^{4}-5 x \right ) y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.840 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-3 x^{2}+x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.733 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+5 x y^{\prime }+3 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.794 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0
\] |
[_Lienard] |
✓ |
0.485 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \,{\mathrm e}^{x} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.786 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (x^{2}+5 x \right ) y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.005 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x \,{\mathrm e}^{x} y^{\prime }+3 \cos \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.801 |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+3 \left (x^{2}+x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.859 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.718 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.842 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (-x^{3}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.702 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.824 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.226 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (4 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.436 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.404 |
|
|
\[
{}y^{\prime } = x^{2} y
\] |
[_separable] |
✓ |
1.606 |
|
|
\[
{}y y^{\prime } = x
\] |
[_separable] |
✓ |
4.452 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+x}{y-y^{2}}
\] |
[_separable] |
✓ |
1.471 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{x -y}}{{\mathrm e}^{x}+1}
\] |
[_separable] |
✓ |
1.803 |
|
|
\[
{}y^{\prime } = y^{2} x^{2}-4 x^{2}
\] |
[_separable] |
✓ |
2.471 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
2.053 |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
2.013 |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
1.652 |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
39.321 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x y+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
72.306 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.477 |
|
|
\[
{}y^{\prime } = \frac {y+x \,{\mathrm e}^{-\frac {2 y}{x}}}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
27.303 |
|
|
\[
{}y^{\prime } = \frac {x -y+2}{x +y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.200 |
|
|
\[
{}y^{\prime } = \frac {2 x +3 y+1}{x -2 y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.103 |
|
|
\[
{}y^{\prime } = \frac {x +y+1}{2 x +2 y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.842 |
|
|
\[
{}y^{\prime } = \frac {\left (x +y-1\right )^{2}}{2 \left (x +2\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
2.336 |
|
|
\[
{}2 x y+\left (x^{2}+3 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
0.283 |
|
|
\[
{}x^{2}+x y+\left (x +y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.240 |
|
|
\[
{}{\mathrm e}^{x}+{\mathrm e}^{y} \left (y+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
0.408 |
|
|
\[
{}\cos \left (x \right ) \cos \left (y\right )^{2}-\sin \left (x \right ) \sin \left (2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
0.552 |
|
|
\[
{}x^{2} y^{3}-x^{3} y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
0.695 |
|
|
\[
{}x +y+\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.447 |
|
|
\[
{}2 y \,{\mathrm e}^{2 x}+2 x \cos \left (y\right )+\left ({\mathrm e}^{2 x}-x^{2} \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.382 |
|
|
\[
{}3 x^{2} \ln \left (x \right )+x^{2}+y+x y^{\prime } = 0
\] |
[_linear] |
✓ |
0.255 |
|
|
\[
{}2 y^{3}+2+3 x y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
0.651 |
|
|
\[
{}\cos \left (x \right ) \cos \left (y\right )-2 \sin \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
0.471 |
|
|
\[
{}5 x^{3} y^{2}+2 y+\left (3 x^{4} y+2 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.456 |
|
|
\[
{}{\mathrm e}^{y}+x \,{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.332 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.825 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } = {\mathrm e}^{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.683 |
|
|
\[
{}y y^{\prime \prime }+4 {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.189 |
|
|
\[
{}y^{\prime \prime }+k^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.630 |
|
|
\[
{}y^{\prime \prime } = y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.261 |
|
|
\[
{}x y^{\prime \prime }-2 y^{\prime } = x^{3}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.963 |
|
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.718 |
|
|
\[
{}y^{\prime \prime } = -\frac {1}{2 {y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
1.702 |
|
|
\[
{}y^{\prime \prime }+\sin \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
245.254 |
|
|
\[
{}y^{\prime \prime }+\sin \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
251.366 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1} \\ y_{2}^{\prime }=y_{1}+y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.519 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2} \\ y_{2}^{\prime }=6 y_{1}+y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.611 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+y_{2} \\ y_{2}^{\prime }=y_{1}+y_{2}+{\mathrm e}^{3 x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.491 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+x y_{3} \\ y_{2}^{\prime }=y_{2}+x^{3} y_{3} \\ y_{3}^{\prime }=2 x y_{1}-y_{2}+{\mathrm e}^{x} y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.043 |
|
|
\[
{}y^{\prime } = 2 x
\] |
[_quadrature] |
✓ |
0.437 |
|
|
\[
{}x y^{\prime } = 2 y
\] |
[_separable] |
✓ |
2.178 |
|
|
\[
{}y y^{\prime } = {\mathrm e}^{2 x}
\] |
[_separable] |
✓ |
2.197 |
|
|
\[
{}y^{\prime } = k y
\] |
[_quadrature] |
✓ |
0.797 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.174 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.948 |
|
|
\[
{}x y^{\prime }+y = y^{\prime } \sqrt {1-y^{2} x^{2}}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
4.357 |
|
|
\[
{}x y^{\prime } = y+x^{2}+y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.698 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
15.191 |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.048 |
|
|
\[
{}x y^{\prime }+y = x^{4} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.723 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x y-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
72.435 |
|
|
\[
{}\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime } = y
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.983 |
|
|
\[
{}1+y^{2}+y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
1.305 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 x}-x
\] |
[_quadrature] |
✓ |
0.473 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.466 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.574 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.494 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \arctan \left (x \right )
\] |
[_quadrature] |
✓ |
0.627 |
|
|
\[
{}x y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.446 |
|
|
\[
{}y^{\prime } = \arcsin \left (x \right )
\] |
[_quadrature] |
✓ |
0.354 |
|
|
\[
{}\sin \left (x \right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.712 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.739 |
|
|
\[
{}\left (x^{2}-3 x +2\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.610 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
0.770 |
|
|
\[
{}y^{\prime } = 2 \sin \left (x \right ) \cos \left (x \right )
\] |
[_quadrature] |
✓ |
0.770 |
|
|
\[
{}y^{\prime } = \ln \left (x \right )
\] |
[_quadrature] |
✓ |
0.470 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.685 |
|