|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.969 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.611 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.127 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.341 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.064 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-2-i\right ) x y^{\prime }+3 i y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.438 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 \pi y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.883 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.075 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+x^{6} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.425 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime }+3 x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.171 |
|
|
\[
{}x y^{\prime \prime }+4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.227 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.967 |
|
|
\[
{}\left (x^{2}+x -2\right )^{2} y^{\prime \prime }+3 \left (x +2\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.444 |
|
|
\[
{}x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.937 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.995 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (4 x^{4}-5 x \right ) y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.117 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-3 x^{2}+x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.002 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+5 y^{\prime } x +3 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.016 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y = 0
\] |
[_Lienard] |
✓ |
0.735 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \,{\mathrm e}^{x} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.056 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (x^{2}+5 x \right ) y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.212 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x \,{\mathrm e}^{x} y^{\prime }+3 \cos \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.003 |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+3 \left (x^{2}+x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.133 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.936 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.089 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (-x^{3}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.952 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.085 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.245 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (4 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.376 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.646 |
|
|
\[
{}y^{\prime } = x^{2} y
\] |
[_separable] |
✓ |
1.625 |
|
|
\[
{}y y^{\prime } = x
\] |
[_separable] |
✓ |
3.699 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+x}{y-y^{2}}
\] |
[_separable] |
✓ |
1.459 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{x -y}}{{\mathrm e}^{x}+1}
\] |
[_separable] |
✓ |
1.767 |
|
|
\[
{}y^{\prime } = x^{2} y^{2}-4 x^{2}
\] |
[_separable] |
✓ |
2.533 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.350 |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
1.489 |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
0.938 |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.621 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x y+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
13.783 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+x y+y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.611 |
|
|
\[
{}y^{\prime } = \frac {y+x \,{\mathrm e}^{-\frac {2 y}{x}}}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
16.133 |
|
|
\[
{}y^{\prime } = \frac {x -y+2}{x +y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.511 |
|
|
\[
{}y^{\prime } = \frac {2 x +3 y+1}{x -2 y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.024 |
|
|
\[
{}y^{\prime } = \frac {x +y+1}{2 x +2 y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.835 |
|
|
\[
{}y^{\prime } = \frac {\left (x +y-1\right )^{2}}{2 \left (x +2\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
2.373 |
|
|
\[
{}2 x y+\left (x^{2}+3 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
0.339 |
|
|
\[
{}x^{2}+x y+\left (x +y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.268 |
|
|
\[
{}{\mathrm e}^{x}+{\mathrm e}^{y} \left (1+y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
0.380 |
|
|
\[
{}\cos \left (x \right ) \cos \left (y\right )^{2}-\sin \left (x \right ) \sin \left (2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
0.483 |
|
|
\[
{}x^{2} y^{3}-x^{3} y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
0.578 |
|
|
\[
{}x +y+\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.401 |
|
|
\[
{}2 y \,{\mathrm e}^{2 x}+2 x \cos \left (y\right )+\left ({\mathrm e}^{2 x}-x^{2} \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.398 |
|
|
\[
{}3 x^{2} \ln \left (x \right )+x^{2}+y+y^{\prime } x = 0
\] |
[_linear] |
✓ |
0.258 |
|
|
\[
{}2 y^{3}+2+3 x y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
0.566 |
|
|
\[
{}\cos \left (x \right ) \cos \left (y\right )-2 \sin \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
0.427 |
|
|
\[
{}5 x^{3} y^{2}+2 y+\left (3 x^{4} y+2 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.413 |
|
|
\[
{}{\mathrm e}^{y}+x \,{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.351 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.090 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } = {\mathrm e}^{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.866 |
|
|
\[
{}y y^{\prime \prime }+4 {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.208 |
|
|
\[
{}y^{\prime \prime }+k^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.748 |
|
|
\[
{}y^{\prime \prime } = y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.662 |
|
|
\[
{}x y^{\prime \prime }-2 y^{\prime } = x^{3}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.144 |
|
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
6.263 |
|
|
\[
{}y^{\prime \prime } = -\frac {1}{2 {y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
3.356 |
|
|
\[
{}y^{\prime \prime }+\sin \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
400.405 |
|
|
\[
{}y^{\prime \prime }+\sin \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
147.454 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1} \\ y_{2}^{\prime }=y_{1}+y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.510 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2} \\ y_{2}^{\prime }=6 y_{1}+y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.648 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+y_{2} \\ y_{2}^{\prime }=y_{1}+y_{2}+{\mathrm e}^{3 x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.559 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+x y_{3} \\ y_{2}^{\prime }=y_{2}+x^{3} y_{3} \\ y_{3}^{\prime }=2 y_{1} x -y_{2}+{\mathrm e}^{x} y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.077 |
|
|
\[
{}y^{\prime } = 2 x
\] |
[_quadrature] |
✓ |
0.451 |
|
|
\[
{}y^{\prime } x = 2 y
\] |
[_separable] |
✓ |
2.247 |
|
|
\[
{}y y^{\prime } = {\mathrm e}^{2 x}
\] |
[_separable] |
✓ |
1.713 |
|
|
\[
{}y^{\prime } = k y
\] |
[_quadrature] |
✓ |
0.705 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.380 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.454 |
|
|
\[
{}y^{\prime } x +y = y^{\prime } \sqrt {1-x^{2} y^{2}}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
4.024 |
|
|
\[
{}y^{\prime } x = y+x^{2}+y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.651 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.375 |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
8.124 |
|
|
\[
{}y^{\prime } x +y = x^{4} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.043 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x y-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
14.026 |
|
|
\[
{}\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime } = y
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.796 |
|
|
\[
{}1+y^{2}+y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
4.421 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 x}-x
\] |
[_quadrature] |
✓ |
0.515 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.505 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.533 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.546 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \arctan \left (x \right )
\] |
[_quadrature] |
✓ |
0.596 |
|
|
\[
{}y^{\prime } x = 1
\] |
[_quadrature] |
✓ |
0.483 |
|
|
\[
{}y^{\prime } = \arcsin \left (x \right )
\] |
[_quadrature] |
✓ |
0.400 |
|
|
\[
{}\sin \left (x \right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.617 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.697 |
|
|
\[
{}\left (x^{2}-3 x +2\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.596 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
0.693 |
|
|
\[
{}y^{\prime } = 2 \sin \left (x \right ) \cos \left (x \right )
\] |
[_quadrature] |
✓ |
0.820 |
|
|
\[
{}y^{\prime } = \ln \left (x \right )
\] |
[_quadrature] |
✓ |
0.421 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.667 |
|