# |
ODE |
CAS classification |
Solved? |
time (sec) |
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.086 |
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (-x^{3}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.954 |
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.066 |
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.246 |
|
\[
{}x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (4 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.470 |
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.634 |
|
\[
{}y^{\prime } = x^{2} y
\] |
[_separable] |
✓ |
1.145 |
|
\[
{}y^{\prime } y = x
\] |
[_separable] |
✓ |
3.020 |
|
\[
{}y^{\prime } = \frac {x^{2}+x}{y-y^{2}}
\] |
[_separable] |
✓ |
1.272 |
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{x -y}}{1+{\mathrm e}^{x}}
\] |
[_separable] |
✓ |
1.430 |
|
\[
{}y^{\prime } = x^{2} y^{2}-4 x^{2}
\] |
[_separable] |
✓ |
3.371 |
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.002 |
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
1.212 |
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
0.976 |
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.597 |
|
\[
{}y^{\prime } = \frac {y^{2}}{x y+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
36.718 |
|
\[
{}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.064 |
|
\[
{}y^{\prime } = \frac {y+x \,{\mathrm e}^{-\frac {2 y}{x}}}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
17.124 |
|
\[
{}y^{\prime } = \frac {x -y+2}{y-1+x}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.569 |
|
\[
{}y^{\prime } = \frac {2 x +3 y+1}{-2 y-1+x}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.076 |
|
\[
{}y^{\prime } = \frac {x +y+1}{2 x +2 y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.298 |
|
\[
{}y^{\prime } = \frac {\left (y-1+x \right )^{2}}{2 \left (x +2\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
2.095 |
|
\[
{}2 x y+\left (x^{2}+3 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
0.235 |
|
\[
{}x^{2}+x y+\left (x +y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.181 |
|
\[
{}{\mathrm e}^{x}+{\mathrm e}^{y} \left (y+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
0.293 |
|
\[
{}\cos \left (x \right ) \cos \left (y\right )^{2}-\sin \left (x \right ) \sin \left (2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
0.403 |
|
\[
{}y^{3} x^{2}-x^{3} y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
0.587 |
|
\[
{}x +y+\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.311 |
|
\[
{}2 y \,{\mathrm e}^{2 x}+2 x \cos \left (y\right )+\left ({\mathrm e}^{2 x}-x^{2} \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.293 |
|
\[
{}3 x^{2} \ln \left (x \right )+x^{2}+y+x y^{\prime } = 0
\] |
[_linear] |
✓ |
0.198 |
|
\[
{}2 y^{3}+2+3 x y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
0.500 |
|
\[
{}\cos \left (x \right ) \cos \left (y\right )-2 \sin \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
0.349 |
|
\[
{}5 x^{3} y^{2}+2 y+\left (3 x^{4} y+2 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.333 |
|
\[
{}{\mathrm e}^{y}+x \,{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.304 |
|
\[
{}y^{\prime \prime }+y^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.408 |
|
\[
{}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime } = {\mathrm e}^{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.830 |
|
\[
{}y y^{\prime \prime }+4 {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.192 |
|
\[
{}y^{\prime \prime }+k^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.639 |
|
\[
{}y^{\prime \prime } = y^{\prime } y
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.619 |
|
\[
{}x y^{\prime \prime }-2 y^{\prime } = x^{3}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.138 |
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.720 |
|
\[
{}y^{\prime \prime } = -\frac {1}{2 {y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
2.638 |
|
\[
{}y^{\prime \prime }+\sin \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
346.226 |
|
\[
{}y^{\prime \prime }+\sin \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
148.853 |
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1} \\ y_{2}^{\prime }=y_{1}+y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.408 |
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2} \\ y_{2}^{\prime }=6 y_{1}+y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.495 |
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+y_{2} \\ y_{2}^{\prime }=y_{1}+y_{2}+{\mathrm e}^{3 x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.556 |
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+x y_{3} \\ y_{2}^{\prime }=y_{2}+x^{3} y_{3} \\ y_{3}^{\prime }=2 x y_{1}-y_{2}+{\mathrm e}^{x} y_{3} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.060 |
|
\[
{}y^{\prime } = 2 x
\] |
[_quadrature] |
✓ |
0.263 |
|
\[
{}x y^{\prime } = 2 y
\] |
[_separable] |
✓ |
1.576 |
|
\[
{}y^{\prime } y = {\mathrm e}^{2 x}
\] |
[_separable] |
✓ |
1.362 |
|
\[
{}y^{\prime } = k y
\] |
[_quadrature] |
✓ |
0.716 |
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.959 |
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.089 |
|
\[
{}x y^{\prime }+y = y^{\prime } \sqrt {1-x^{2} y^{2}}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
4.122 |
|
\[
{}x y^{\prime } = y+x^{2}+y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.391 |
|
\[
{}y^{\prime } = \frac {x y}{y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.820 |
|
\[
{}2 x y y^{\prime } = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.406 |
|
\[
{}x y^{\prime }+y = x^{4} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.918 |
|
\[
{}y^{\prime } = \frac {y^{2}}{x y-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.066 |
|
\[
{}\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime } = y
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.609 |
|
\[
{}1+y^{2}+y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
3.979 |
|
\[
{}y^{\prime } = {\mathrm e}^{3 x}-x
\] |
[_quadrature] |
✓ |
0.305 |
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.316 |
|
\[
{}\left (x +1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.340 |
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.347 |
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \arctan \left (x \right )
\] |
[_quadrature] |
✓ |
0.402 |
|
\[
{}x y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.309 |
|
\[
{}y^{\prime } = \arcsin \left (x \right )
\] |
[_quadrature] |
✓ |
0.296 |
|
\[
{}\sin \left (x \right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.461 |
|
\[
{}\left (x^{3}+1\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.585 |
|
\[
{}\left (x^{2}-3 x +2\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.378 |
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
0.556 |
|
\[
{}y^{\prime } = 2 \sin \left (x \right ) \cos \left (x \right )
\] |
[_quadrature] |
✓ |
0.543 |
|
\[
{}y^{\prime } = \ln \left (x \right )
\] |
[_quadrature] |
✓ |
0.510 |
|
\[
{}\left (x^{2}-1\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.461 |
|
\[
{}x \left (x^{2}-4\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.618 |
|
\[
{}\left (x +1\right ) \left (x^{2}+1\right ) y^{\prime } = 2 x^{2}+x
\] |
[_quadrature] |
✓ |
1.095 |
|
\[
{}y^{\prime } = 2 x y+1
\] |
[_linear] |
✓ |
0.895 |
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.828 |
|
\[
{}y^{\prime } = \frac {2 x y^{2}}{1-x^{2} y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.401 |
|
\[
{}2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
\[
{}x^{5} y^{\prime }+y^{5} = 0
\] |
[_separable] |
✓ |
4.889 |
|
\[
{}y^{\prime } = 4 x y
\] |
[_separable] |
✓ |
1.158 |
|
\[
{}y^{\prime }+\tan \left (x \right ) y = 0
\] |
[_separable] |
✓ |
1.344 |
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+1+y^{2} = 0
\] |
[_separable] |
✓ |
1.820 |
|
\[
{}y \ln \left (y\right )-x y^{\prime } = 0
\] |
[_separable] |
✓ |
1.617 |
|
\[
{}x y^{\prime } = \left (-4 x^{2}+1\right ) \tan \left (y\right )
\] |
[_separable] |
✓ |
2.049 |
|
\[
{}y^{\prime } \sin \left (y\right ) = x^{2}
\] |
[_separable] |
✓ |
1.331 |
|
\[
{}y^{\prime }-\tan \left (x \right ) y = 0
\] |
[_separable] |
✓ |
1.387 |
|
\[
{}x y y^{\prime } = y-1
\] |
[_separable] |
✓ |
1.364 |
|
\[
{}x y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.192 |
|
\[
{}y^{\prime } y = x +1
\] |
[_separable] |
✓ |
2.991 |
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✓ |
1.529 |
|
\[
{}\frac {y^{\prime }}{x^{2}+1} = \frac {x}{y}
\] |
[_separable] |
✓ |
1.819 |
|
\[
{}y^{2} y^{\prime } = x +2
\] |
[_separable] |
✓ |
2.516 |
|
\[
{}y^{\prime } = x^{2} y^{2}
\] |
[_separable] |
✓ |
2.085 |
|
\[
{}\left (y+1\right ) y^{\prime } = -x^{2}+1
\] |
[_separable] |
✓ |
1.874 |
|
\[
{}\frac {y^{\prime \prime }}{y^{\prime }} = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.620 |
|
\[
{}y^{\prime \prime } y^{\prime } = x \left (x +1\right )
\] |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
1.790 |
|