|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\sin \left (x +y\right )-y^{\prime } y = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.816 |
|
|
\[
{}y^{\prime }-y^{3} = 8
\] |
[_quadrature] |
✓ |
2.435 |
|
|
\[
{}x^{2} y^{\prime }+x y^{2} = x
\] |
[_separable] |
✓ |
1.402 |
|
|
\[
{}y^{\prime }-y^{2} = x
\] |
[[_Riccati, _special]] |
✓ |
0.961 |
|
|
\[
{}y^{3}-25 y+y^{\prime } = 0
\] |
[_quadrature] |
✓ |
2.857 |
|
|
\[
{}\left (-2+x \right ) y^{\prime } = y+3
\] |
[_separable] |
✓ |
1.471 |
|
|
\[
{}\left (y-2\right ) y^{\prime } = x -3
\] |
[_separable] |
✓ |
2.869 |
|
|
\[
{}y^{\prime }+2 y-y^{2} = -2
\] |
[_quadrature] |
✓ |
1.031 |
|
|
\[
{}y^{\prime }+\left (8-x \right ) y-y^{2} = -8 x
\] |
[_Riccati] |
✓ |
1.535 |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
1.353 |
|
|
\[
{}y^{\prime } = 3 y^{2}-y^{2} \sin \left (x \right )
\] |
[_separable] |
✓ |
1.772 |
|
|
\[
{}y^{\prime } = 3 x -y \sin \left (x \right )
\] |
[_linear] |
✓ |
1.862 |
|
|
\[
{}x y^{\prime } = \left (x -y\right )^{2}
\] |
[_rational, _Riccati] |
✓ |
1.569 |
|
|
\[
{}y^{\prime } = \sqrt {x^{2}+1}
\] |
[_quadrature] |
✓ |
0.357 |
|
|
\[
{}y^{\prime }+4 y = 8
\] |
[_quadrature] |
✓ |
1.070 |
|
|
\[
{}y^{\prime }+x y = 4 x
\] |
[_separable] |
✓ |
1.396 |
|
|
\[
{}y^{\prime }+4 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.056 |
|
|
\[
{}y^{\prime } = x y-3 x -2 y+6
\] |
[_separable] |
✓ |
1.282 |
|
|
\[
{}y^{\prime } = \sin \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.349 |
|
|
\[
{}y^{\prime } y = {\mathrm e}^{x -3 y^{2}}
\] |
[_separable] |
✓ |
1.478 |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
2.962 |
|
|
\[
{}y^{\prime } = y^{2}+9
\] |
[_quadrature] |
✓ |
0.980 |
|
|
\[
{}x y y^{\prime } = y^{2}+9
\] |
[_separable] |
✓ |
2.445 |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
1.809 |
|
|
\[
{}\cos \left (y\right ) y^{\prime } = \sin \left (x \right )
\] |
[_separable] |
✓ |
1.728 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x -3 y}
\] |
[_separable] |
✓ |
1.732 |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
4.293 |
|
|
\[
{}y^{\prime } = 2 x -1+2 x y-y
\] |
[_separable] |
✓ |
1.503 |
|
|
\[
{}y^{\prime } y = x y^{2}+x
\] |
[_separable] |
✓ |
2.852 |
|
|
\[
{}y^{\prime } y = 3 \sqrt {x y^{2}+9 x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
3.803 |
|
|
\[
{}y^{\prime } = x y-4 x
\] |
[_separable] |
✓ |
1.194 |
|
|
\[
{}y^{\prime }-4 y = 2
\] |
[_quadrature] |
✓ |
0.962 |
|
|
\[
{}y^{\prime } y = x y^{2}-9 x
\] |
[_separable] |
✓ |
1.888 |
|
|
\[
{}y^{\prime } = \sin \left (y\right )
\] |
[_quadrature] |
✓ |
1.444 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x +y^{2}}
\] |
[_separable] |
✓ |
1.187 |
|
|
\[
{}y^{\prime } = 200 y-2 y^{2}
\] |
[_quadrature] |
✓ |
1.983 |
|
|
\[
{}y^{\prime } = x y-4 x
\] |
[_separable] |
✓ |
1.148 |
|
|
\[
{}y^{\prime } = x y-3 x -2 y+6
\] |
[_separable] |
✓ |
1.273 |
|
|
\[
{}y^{\prime } = 3 y^{2}-y^{2} \sin \left (x \right )
\] |
[_separable] |
✓ |
1.844 |
|
|
\[
{}y^{\prime } = \tan \left (y\right )
\] |
[_quadrature] |
✓ |
1.122 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.260 |
|
|
\[
{}y^{\prime } = \frac {6 x^{2}+4}{3 y^{2}-4 y}
\] |
[_separable] |
✓ |
1.361 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
1.873 |
|
|
\[
{}\left (y^{2}-1\right ) y^{\prime } = 4 x y^{2}
\] |
[_separable] |
✓ |
11.935 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-y}
\] |
[_quadrature] |
✓ |
0.924 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-y}+1
\] |
[_quadrature] |
✓ |
1.284 |
|
|
\[
{}y^{\prime } = 3 x y^{3}
\] |
[_separable] |
✓ |
2.251 |
|
|
\[
{}y^{\prime } = \frac {2+\sqrt {x}}{2+\sqrt {y}}
\] |
[_separable] |
✓ |
1.570 |
|
|
\[
{}y^{\prime }-3 x^{2} y^{2} = -3 x^{2}
\] |
[_separable] |
✓ |
3.053 |
|
|
\[
{}y^{\prime }-3 x^{2} y^{2} = 3 x^{2}
\] |
[_separable] |
✓ |
3.187 |
|
|
\[
{}y^{\prime } = 200 y-2 y^{2}
\] |
[_quadrature] |
✓ |
1.863 |
|
|
\[
{}y^{\prime }-2 y = -10
\] |
[_quadrature] |
✓ |
1.263 |
|
|
\[
{}y^{\prime } y = \sin \left (x \right )
\] |
[_separable] |
✓ |
2.396 |
|
|
\[
{}y^{\prime } = 2 x -1+2 x y-y
\] |
[_separable] |
✓ |
1.368 |
|
|
\[
{}x y^{\prime } = y^{2}-y
\] |
[_separable] |
✓ |
2.102 |
|
|
\[
{}x y^{\prime } = y^{2}-y
\] |
[_separable] |
✓ |
2.133 |
|
|
\[
{}y^{\prime } = \frac {y^{2}-1}{x y}
\] |
[_separable] |
✓ |
4.074 |
|
|
\[
{}\left (y^{2}-1\right ) y^{\prime } = 4 x y
\] |
[_separable] |
✓ |
1.891 |
|
|
\[
{}x^{2} y^{\prime }+3 x^{2} y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.684 |
|
|
\[
{}y^{2} y^{\prime }+3 x^{2} y = \sin \left (x \right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.018 |
|
|
\[
{}y^{\prime }-x y^{2} = \sqrt {x}
\] |
[_Riccati] |
✓ |
1.632 |
|
|
\[
{}y^{\prime } = 1+\left (x y+3 y\right )^{2}
\] |
[_Riccati] |
✓ |
5.441 |
|
|
\[
{}y^{\prime } = 1+x y+3 y
\] |
[_linear] |
✓ |
1.158 |
|
|
\[
{}y^{\prime } = 4 y+8
\] |
[_quadrature] |
✓ |
0.961 |
|
|
\[
{}y^{\prime }-{\mathrm e}^{2 x} = 0
\] |
[_quadrature] |
✓ |
0.311 |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
1.385 |
|
|
\[
{}y^{\prime }+4 y = y^{3}
\] |
[_quadrature] |
✓ |
3.338 |
|
|
\[
{}x y^{\prime }+\cos \left (x^{2}\right ) = 827 y
\] |
[_linear] |
✓ |
1.995 |
|
|
\[
{}y^{\prime }+2 y = 6
\] |
[_quadrature] |
✓ |
1.119 |
|
|
\[
{}y^{\prime }+2 y = 20 \,{\mathrm e}^{3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.109 |
|
|
\[
{}y^{\prime } = 4 y+16 x
\] |
[[_linear, ‘class A‘]] |
✓ |
0.982 |
|
|
\[
{}y^{\prime }-2 x y = x
\] |
[_separable] |
✓ |
1.116 |
|
|
\[
{}x y^{\prime }+3 y-10 x^{2} = 0
\] |
[_linear] |
✓ |
1.398 |
|
|
\[
{}x^{2} y^{\prime }+2 x y = \sin \left (x \right )
\] |
[_linear] |
✓ |
1.277 |
|
|
\[
{}x y^{\prime } = \sqrt {x}+3 y
\] |
[_linear] |
✓ |
1.416 |
|
|
\[
{}y \sin \left (x \right )+y^{\prime } \cos \left (x \right ) = \cos \left (x \right )^{2}
\] |
[_linear] |
✓ |
2.293 |
|
|
\[
{}x y^{\prime }+\left (5 x +2\right ) y = \frac {20}{x}
\] |
[_linear] |
✓ |
2.098 |
|
|
\[
{}2 \sqrt {x}\, y^{\prime }+y = 2 x \,{\mathrm e}^{-\sqrt {x}}
\] |
[_linear] |
✓ |
2.712 |
|
|
\[
{}y^{\prime }-3 y = 6
\] |
[_quadrature] |
✓ |
1.319 |
|
|
\[
{}y^{\prime }-3 y = 6
\] |
[_quadrature] |
✓ |
1.028 |
|
|
\[
{}y^{\prime }+5 y = {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.378 |
|
|
\[
{}x y^{\prime }+3 y = 20 x^{2}
\] |
[_linear] |
✓ |
1.824 |
|
|
\[
{}x y^{\prime } = y+x^{2} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.566 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (3+3 x^{2}-y\right )
\] |
[_linear] |
✓ |
4.116 |
|
|
\[
{}y^{\prime }+6 x y = \sin \left (x \right )
\] |
[_linear] |
✓ |
1.638 |
|
|
\[
{}x^{2} y^{\prime }+x y = \sqrt {x}\, \sin \left (x \right )
\] |
[_linear] |
✓ |
2.056 |
|
|
\[
{}-y+x y^{\prime } = x^{2} {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
1.625 |
|
|
\[
{}y^{\prime } = \frac {1}{\left (3 x +3 y+2\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
5.666 |
|
|
\[
{}y^{\prime } = \frac {\left (-2 y+3 x \right )^{2}+1}{-2 y+3 x}+\frac {3}{2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
10.996 |
|
|
\[
{}\cos \left (-4 y+8 x -3\right ) y^{\prime } = 2+2 \cos \left (-4 y+8 x -3\right )
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
122.847 |
|
|
\[
{}y^{\prime } = 1+\left (y-x \right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
3.171 |
|
|
\[
{}x^{2} y^{\prime }-x y = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.850 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\frac {x}{y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.608 |
|
|
\[
{}\cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right ) = 1+\sin \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.479 |
|
|
\[
{}y^{\prime } = \frac {x -y}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.010 |
|
|
\[
{}y^{\prime }+3 y = 3 y^{3}
\] |
[_quadrature] |
✓ |
3.409 |
|
|
\[
{}y^{\prime }-\frac {3 y}{x} = \frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.893 |
|
|
\[
{}y^{\prime }+3 y \cot \left (x \right ) = 6 \cos \left (x \right ) y^{{2}/{3}}
\] |
[_Bernoulli] |
✓ |
3.879 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = \frac {1}{y}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
3.760 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\frac {x^{2}}{y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.808 |
|