|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime }-2 x y = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.373 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.959 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.376 |
|
|
\[
{}x y^{\prime }+y = \frac {1}{y^{2}}
\] |
[_separable] |
✓ |
4.215 |
|
|
\[
{}1+{y^{\prime }}^{2} = \frac {1}{y^{2}}
\] |
[_quadrature] |
✓ |
0.453 |
|
|
\[
{}y^{\prime \prime } = 2 y {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.214 |
|
|
\[
{}\left (1-x y\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.592 |
|
|
\[
{}y^{\prime \prime }+9 y = 5
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.615 |
|
|
\[
{}y^{\prime }+2 y = 3 x
\] |
[[_linear, ‘class A‘]] |
✓ |
1.289 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.937 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.193 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.207 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.192 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.573 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.608 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✗ |
1.786 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.513 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.959 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.980 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.961 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.000 |
|
|
\[
{}y^{\prime } = 1-x y
\] |
[_linear] |
✓ |
1.327 |
|
|
\[
{}y^{\prime } = 1-x y
\] |
[_linear] |
✓ |
1.374 |
|
|
\[
{}y^{\prime } = 1-x y
\] |
[_linear] |
✓ |
1.323 |
|
|
\[
{}y^{\prime } = 1-x y
\] |
[_linear] |
✓ |
1.305 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \cos \left (y\right )
\] |
[_separable] |
✓ |
4.449 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \cos \left (y\right )
\] |
[_separable] |
✓ |
4.273 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \cos \left (y\right )
\] |
[_separable] |
✓ |
4.329 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \cos \left (y\right )
\] |
[_separable] |
✓ |
3.218 |
|
|
\[
{}y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.644 |
|
|
\[
{}y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.629 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.524 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.483 |
|
|
\[
{}y y^{\prime } = -x
\] |
[_separable] |
✓ |
4.427 |
|
|
\[
{}y y^{\prime } = -x
\] |
[_separable] |
✓ |
10.550 |
|
|
\[
{}y^{\prime } = \frac {1}{y}
\] |
[_quadrature] |
✓ |
2.205 |
|
|
\[
{}y^{\prime } = \frac {1}{y}
\] |
[_quadrature] |
✓ |
2.071 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{5}+y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.600 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{5}+y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.631 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{y}
\] |
[_separable] |
✓ |
3.106 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{y}
\] |
[_separable] |
✓ |
3.267 |
|
|
\[
{}y^{\prime } = y-\cos \left (\frac {\pi x}{2}\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.095 |
|
|
\[
{}y^{\prime } = y-\cos \left (\frac {\pi x}{2}\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.084 |
|
|
\[
{}y^{\prime } = 1-\frac {y}{x}
\] |
[_linear] |
✓ |
2.986 |
|
|
\[
{}y^{\prime } = 1-\frac {y}{x}
\] |
[_linear] |
✓ |
2.982 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.214 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.148 |
|
|
\[
{}y^{\prime } = x \left (y-4\right )^{2}-2
\] |
[_Riccati] |
✓ |
2.178 |
|
|
\[
{}y^{\prime } = x^{2}-2 y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.325 |
|
|
\[
{}y^{\prime } = y-y^{3}
\] |
[_quadrature] |
✓ |
4.316 |
|
|
\[
{}y^{\prime } = y^{2}-y^{4}
\] |
[_quadrature] |
✓ |
1.883 |
|
|
\[
{}y^{\prime } = y^{2}-3 y
\] |
[_quadrature] |
✓ |
1.923 |
|
|
\[
{}y^{\prime } = y^{2}-y^{3}
\] |
[_quadrature] |
✓ |
17.039 |
|
|
\[
{}y^{\prime } = \left (y-2\right )^{4}
\] |
[_quadrature] |
✓ |
2.187 |
|
|
\[
{}y^{\prime } = 10+3 y-y^{2}
\] |
[_quadrature] |
✓ |
2.108 |
|
|
\[
{}y^{\prime } = y^{2} \left (4-y^{2}\right )
\] |
[_quadrature] |
✓ |
1.914 |
|
|
\[
{}y^{\prime } = y \left (2-y\right ) \left (4-y\right )
\] |
[_quadrature] |
✓ |
4.015 |
|
|
\[
{}y^{\prime } = y \ln \left (y+2\right )
\] |
[_quadrature] |
✓ |
2.204 |
|
|
\[
{}y^{\prime } = \left (y \,{\mathrm e}^{y}-9 y\right ) {\mathrm e}^{-y}
\] |
[_quadrature] |
✓ |
2.178 |
|
|
\[
{}y^{\prime } = \frac {2 y}{\pi }-\sin \left (y\right )
\] |
[_quadrature] |
✓ |
2.135 |
|
|
\[
{}y^{\prime } = y^{2}-y-6
\] |
[_quadrature] |
✓ |
1.710 |
|
|
\[
{}m v^{\prime } = m g -k v^{2}
\] |
[_quadrature] |
✓ |
2.568 |
|
|
\[
{}y^{\prime } = \sin \left (5 x \right )
\] |
[_quadrature] |
✓ |
0.573 |
|
|
\[
{}y^{\prime } = \left (x +1\right )^{2}
\] |
[_quadrature] |
✓ |
0.459 |
|
|
\[
{}1+{\mathrm e}^{3 x} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.605 |
|
|
\[
{}y^{\prime }-\left (y-1\right )^{2} = 0
\] |
[_quadrature] |
✓ |
1.128 |
|
|
\[
{}x y^{\prime } = 4 y
\] |
[_separable] |
✓ |
2.264 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
2.179 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 x +2 y}
\] |
[_separable] |
✓ |
2.903 |
|
|
\[
{}{\mathrm e}^{x} y y^{\prime } = {\mathrm e}^{-y}+{\mathrm e}^{-2 x -y}
\] |
[_separable] |
✓ |
1.755 |
|
|
\[
{}y \ln \left (x \right ) y^{\prime } = \frac {\left (y+1\right )^{2}}{x^{2}}
\] |
[_separable] |
✓ |
2.435 |
|
|
\[
{}y^{\prime } = \frac {\left (2 y+3\right )^{2}}{\left (4 x +5\right )^{2}}
\] |
[_separable] |
✓ |
2.908 |
|
|
\[
{}\csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.178 |
|
|
\[
{}\sin \left (3 x \right )+2 y \cos \left (3 x \right )^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
14.938 |
|
|
\[
{}\left (1+{\mathrm e}^{y}\right )^{2} {\mathrm e}^{-y}+\left ({\mathrm e}^{x}+1\right )^{3} {\mathrm e}^{-x} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.740 |
|
|
\[
{}x \sqrt {1+y^{2}} = y \sqrt {x^{2}+1}\, y^{\prime }
\] |
[_separable] |
✓ |
4.559 |
|
|
\[
{}s^{\prime } = k s
\] |
[_quadrature] |
✓ |
0.807 |
|
|
\[
{}q^{\prime } = k \left (q-70\right )
\] |
[_quadrature] |
✓ |
0.803 |
|
|
\[
{}p^{\prime } = p-p^{2}
\] |
[_quadrature] |
✓ |
2.309 |
|
|
\[
{}n^{\prime }+n = n t \,{\mathrm e}^{t +2}
\] |
[_separable] |
✓ |
2.098 |
|
|
\[
{}y^{\prime } = \frac {x y+3 x -y-3}{x y-2 x +4 y-8}
\] |
[_separable] |
✓ |
1.878 |
|
|
\[
{}y^{\prime } = \frac {x y+2 y-x -2}{x y-3 y+x -3}
\] |
[_separable] |
✓ |
1.918 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
33.945 |
|
|
\[
{}\left ({\mathrm e}^{x}+{\mathrm e}^{-x}\right ) y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
2.304 |
|
|
\[
{}x^{\prime } = 4 x^{2}+4
\] |
[_quadrature] |
✓ |
101.785 |
|
|
\[
{}y^{\prime } = \frac {y^{2}-1}{x^{2}-1}
\] |
[_separable] |
✓ |
2.474 |
|
|
\[
{}x^{2} y^{\prime } = y-x y
\] |
[_separable] |
✓ |
2.053 |
|
|
\[
{}y^{\prime }+2 y = 1
\] |
[_quadrature] |
✓ |
2.007 |
|
|
\[
{}\sqrt {1-y^{2}}-\sqrt {-x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
18.102 |
|
|
\[
{}\left (x^{4}+1\right ) y^{\prime }+x \left (1+4 y^{2}\right ) = 0
\] |
[_separable] |
✓ |
3.312 |
|
|
\[
{}y^{\prime } = -y \ln \left (y\right )
\] |
[_quadrature] |
✓ |
1.579 |
|
|
\[
{}x \sinh \left (y\right ) y^{\prime } = \cosh \left (y\right )
\] |
[_separable] |
✓ |
2.547 |
|
|
\[
{}y^{\prime } = y \,{\mathrm e}^{-x^{2}}
\] |
[_separable] |
✓ |
1.778 |
|
|
\[
{}y^{\prime } = y^{2} \sin \left (x^{2}\right )
\] |
[_separable] |
✓ |
3.655 |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) \sqrt {1+\cos \left (x^{3}\right )}
\] |
[_separable] |
✓ |
77.023 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{-2 y} \sin \left (x \right )}{x^{2}+1}
\] |
[_separable] |
✓ |
3.052 |
|
|
\[
{}y^{\prime } = \frac {3 x +1}{2 y}
\] |
[_separable] |
✓ |
4.184 |
|
|
\[
{}\left (2 y-2\right ) y^{\prime } = 3 x^{2}+4 x +2
\] |
[_separable] |
✓ |
2.206 |
|
|
\[
{}{\mathrm e}^{y}-{\mathrm e}^{-x} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.318 |
|
|
\[
{}\sin \left (x \right )+y y^{\prime } = 0
\] |
[_separable] |
✓ |
3.283 |
|