|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime }-2 x y = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.323 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.160 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.671 |
|
|
\[
{}y^{\prime } x +y = \frac {1}{y^{2}}
\] |
[_separable] |
✓ |
3.893 |
|
|
\[
{}1+{y^{\prime }}^{2} = \frac {1}{y^{2}}
\] |
[_quadrature] |
✓ |
0.569 |
|
|
\[
{}y^{\prime \prime } = 2 y {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.279 |
|
|
\[
{}\left (1-x y\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.638 |
|
|
\[
{}y^{\prime \prime }+9 y = 5
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.793 |
|
|
\[
{}y^{\prime }+2 y = 3 x
\] |
[[_linear, ‘class A‘]] |
✓ |
1.293 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.227 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.481 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.527 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.502 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.611 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.806 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✗ |
1.642 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.552 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.934 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.963 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.965 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.012 |
|
|
\[
{}y^{\prime } = 1-x y
\] |
[_linear] |
✓ |
1.466 |
|
|
\[
{}y^{\prime } = 1-x y
\] |
[_linear] |
✓ |
1.559 |
|
|
\[
{}y^{\prime } = 1-x y
\] |
[_linear] |
✓ |
1.537 |
|
|
\[
{}y^{\prime } = 1-x y
\] |
[_linear] |
✓ |
1.468 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \cos \left (y\right )
\] |
[_separable] |
✓ |
4.072 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \cos \left (y\right )
\] |
[_separable] |
✓ |
3.919 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \cos \left (y\right )
\] |
[_separable] |
✓ |
3.723 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \cos \left (y\right )
\] |
[_separable] |
✓ |
2.945 |
|
|
\[
{}y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.596 |
|
|
\[
{}y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.585 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.477 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.510 |
|
|
\[
{}y y^{\prime } = -x
\] |
[_separable] |
✓ |
4.925 |
|
|
\[
{}y y^{\prime } = -x
\] |
[_separable] |
✓ |
6.454 |
|
|
\[
{}y^{\prime } = \frac {1}{y}
\] |
[_quadrature] |
✓ |
2.538 |
|
|
\[
{}y^{\prime } = \frac {1}{y}
\] |
[_quadrature] |
✓ |
2.423 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{5}+y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.626 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{5}+y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.631 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{y}
\] |
[_separable] |
✓ |
3.020 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{y}
\] |
[_separable] |
✓ |
3.194 |
|
|
\[
{}y^{\prime } = y-\cos \left (\frac {\pi x}{2}\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.031 |
|
|
\[
{}y^{\prime } = y-\cos \left (\frac {\pi x}{2}\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.975 |
|
|
\[
{}y^{\prime } = 1-\frac {y}{x}
\] |
[_linear] |
✓ |
3.177 |
|
|
\[
{}y^{\prime } = 1-\frac {y}{x}
\] |
[_linear] |
✓ |
3.178 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.191 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.069 |
|
|
\[
{}y^{\prime } = x \left (y-4\right )^{2}-2
\] |
[_Riccati] |
✓ |
2.074 |
|
|
\[
{}y^{\prime } = x^{2}-2 y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.274 |
|
|
\[
{}y^{\prime } = y-y^{3}
\] |
[_quadrature] |
✓ |
3.827 |
|
|
\[
{}y^{\prime } = y^{2}-y^{4}
\] |
[_quadrature] |
✓ |
1.635 |
|
|
\[
{}y^{\prime } = y^{2}-3 y
\] |
[_quadrature] |
✓ |
1.805 |
|
|
\[
{}y^{\prime } = y^{2}-y^{3}
\] |
[_quadrature] |
✓ |
3.737 |
|
|
\[
{}y^{\prime } = \left (y-2\right )^{4}
\] |
[_quadrature] |
✓ |
1.971 |
|
|
\[
{}y^{\prime } = 10+3 y-y^{2}
\] |
[_quadrature] |
✓ |
1.776 |
|
|
\[
{}y^{\prime } = y^{2} \left (4-y^{2}\right )
\] |
[_quadrature] |
✓ |
1.695 |
|
|
\[
{}y^{\prime } = y \left (2-y\right ) \left (4-y\right )
\] |
[_quadrature] |
✓ |
220.221 |
|
|
\[
{}y^{\prime } = y \ln \left (y+2\right )
\] |
[_quadrature] |
✓ |
1.366 |
|
|
\[
{}y^{\prime } = \left (y \,{\mathrm e}^{y}-9 y\right ) {\mathrm e}^{-y}
\] |
[_quadrature] |
✓ |
1.428 |
|
|
\[
{}y^{\prime } = \frac {2 y}{\pi }-\sin \left (y\right )
\] |
[_quadrature] |
✓ |
1.496 |
|
|
\[
{}y^{\prime } = y^{2}-y-6
\] |
[_quadrature] |
✓ |
1.592 |
|
|
\[
{}m v^{\prime } = m g -k v^{2}
\] |
[_quadrature] |
✓ |
0.830 |
|
|
\[
{}y^{\prime } = \sin \left (5 x \right )
\] |
[_quadrature] |
✓ |
0.544 |
|
|
\[
{}y^{\prime } = \left (x +1\right )^{2}
\] |
[_quadrature] |
✓ |
0.454 |
|
|
\[
{}1+{\mathrm e}^{3 x} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.563 |
|
|
\[
{}y^{\prime }-\left (-1+y\right )^{2} = 0
\] |
[_quadrature] |
✓ |
1.142 |
|
|
\[
{}y^{\prime } x = 4 y
\] |
[_separable] |
✓ |
2.257 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
1.943 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 x +2 y}
\] |
[_separable] |
✓ |
2.543 |
|
|
\[
{}{\mathrm e}^{x} y y^{\prime } = {\mathrm e}^{-y}+{\mathrm e}^{-2 x -y}
\] |
[_separable] |
✗ |
2.835 |
|
|
\[
{}y \ln \left (x \right ) y^{\prime } = \frac {\left (1+y\right )^{2}}{x^{2}}
\] |
[_separable] |
✓ |
1.885 |
|
|
\[
{}y^{\prime } = \frac {\left (2 y+3\right )^{2}}{\left (4 x +5\right )^{2}}
\] |
[_separable] |
✓ |
2.635 |
|
|
\[
{}\csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.644 |
|
|
\[
{}\sin \left (3 x \right )+2 y \cos \left (3 x \right )^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
8.865 |
|
|
\[
{}\left (1+{\mathrm e}^{y}\right )^{2} {\mathrm e}^{-y}+\left ({\mathrm e}^{x}+1\right )^{3} {\mathrm e}^{-x} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.584 |
|
|
\[
{}x \sqrt {1+y^{2}} = y \sqrt {x^{2}+1}\, y^{\prime }
\] |
[_separable] |
✓ |
2.952 |
|
|
\[
{}s^{\prime } = k s
\] |
[_quadrature] |
✓ |
0.694 |
|
|
\[
{}q^{\prime } = k \left (q-70\right )
\] |
[_quadrature] |
✓ |
0.657 |
|
|
\[
{}p^{\prime } = p-p^{2}
\] |
[_quadrature] |
✓ |
1.927 |
|
|
\[
{}n^{\prime }+n = n t \,{\mathrm e}^{t +2}
\] |
[_separable] |
✓ |
1.954 |
|
|
\[
{}y^{\prime } = \frac {x y+3 x -y-3}{x y-2 x +4 y-8}
\] |
[_separable] |
✓ |
1.719 |
|
|
\[
{}y^{\prime } = \frac {x y+2 y-x -2}{x y-3 y+x -3}
\] |
[_separable] |
✓ |
1.734 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
34.191 |
|
|
\[
{}\left ({\mathrm e}^{x}+{\mathrm e}^{-x}\right ) y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
2.062 |
|
|
\[
{}x^{\prime } = 4 x^{2}+4
\] |
[_quadrature] |
✓ |
1.563 |
|
|
\[
{}y^{\prime } = \frac {y^{2}-1}{x^{2}-1}
\] |
[_separable] |
✓ |
2.079 |
|
|
\[
{}x^{2} y^{\prime } = y-x y
\] |
[_separable] |
✓ |
2.944 |
|
|
\[
{}y^{\prime }+2 y = 1
\] |
[_quadrature] |
✓ |
0.926 |
|
|
\[
{}\sqrt {1-y^{2}}-\sqrt {-x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
20.073 |
|
|
\[
{}\left (x^{4}+1\right ) y^{\prime }+x \left (1+4 y^{2}\right ) = 0
\] |
[_separable] |
✓ |
2.659 |
|
|
\[
{}y^{\prime } = -y \ln \left (y\right )
\] |
[_quadrature] |
✓ |
7.122 |
|
|
\[
{}x \sinh \left (y\right ) y^{\prime } = \cosh \left (y\right )
\] |
[_separable] |
✓ |
1.906 |
|
|
\[
{}y^{\prime } = y \,{\mathrm e}^{-x^{2}}
\] |
[_separable] |
✓ |
1.741 |
|
|
\[
{}y^{\prime } = y^{2} \sin \left (x^{2}\right )
\] |
[_separable] |
✓ |
3.257 |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) \sqrt {1+\cos \left (x^{3}\right )}
\] |
[_separable] |
✓ |
503.626 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{-2 y} \sin \left (x \right )}{x^{2}+1}
\] |
[_separable] |
✓ |
4.035 |
|
|
\[
{}y^{\prime } = \frac {1+3 x}{2 y}
\] |
[_separable] |
✓ |
5.861 |
|
|
\[
{}\left (2 y-2\right ) y^{\prime } = 3 x^{2}+4 x +2
\] |
[_separable] |
✓ |
3.574 |
|
|
\[
{}{\mathrm e}^{y}-{\mathrm e}^{-x} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.118 |
|
|
\[
{}\sin \left (x \right )+y y^{\prime } = 0
\] |
[_separable] |
✓ |
2.503 |
|