| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }-y^{2}&=x \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
2.532 |
|
| \begin{align*}
y^{3}-25 y+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.139 |
|
| \begin{align*}
\left (x -2\right ) y^{\prime }&=3+y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.239 |
|
| \begin{align*}
\left (y-2\right ) y^{\prime }&=x -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.777 |
|
| \begin{align*}
y^{\prime }+2 y-y^{2}&=-2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.307 |
|
| \begin{align*}
y^{\prime }+\left (8-x \right ) y-y^{2}&=-8 x \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
2.500 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.303 |
|
| \begin{align*}
y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.398 |
|
| \begin{align*}
y^{\prime }&=3 x -y \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.232 |
|
| \begin{align*}
y^{\prime } x&=\left (x -y\right )^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
72.385 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x^{2}+1} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.214 |
|
| \begin{align*}
y^{\prime }+4 y&=8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
y^{\prime }+y x&=4 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.779 |
|
| \begin{align*}
y^{\prime }+4 y&=x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.664 |
|
| \begin{align*}
y^{\prime }&=y x -3 x -2 y+6 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.042 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.143 |
|
| \begin{align*}
y^{\prime } y&={\mathrm e}^{x -3 y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.474 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 3.369 |
|
| \begin{align*}
y^{\prime }&=y^{2}+9 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.672 |
|
| \begin{align*}
x y^{\prime } y&=y^{2}+9 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.635 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.051 |
|
| \begin{align*}
y^{\prime } \cos \left (y\right )&=\sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.642 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 x -3 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.641 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.577 |
|
| \begin{align*}
y^{\prime }&=2 x -1+2 y x -y \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.687 |
|
| \begin{align*}
y^{\prime } y&=x y^{2}+x \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.660 |
|
| \begin{align*}
y^{\prime } y&=3 \sqrt {x y^{2}+9 x} \\
y \left (1\right ) &= 4 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.269 |
|
| \begin{align*}
y^{\prime }&=y x -4 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.884 |
|
| \begin{align*}
y^{\prime }-4 y&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.377 |
|
| \begin{align*}
y^{\prime } y&=x y^{2}-9 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.329 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
27.312 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.226 |
|
| \begin{align*}
y^{\prime }&=200 y-2 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| \begin{align*}
y^{\prime }&=y x -4 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.928 |
|
| \begin{align*}
y^{\prime }&=y x -3 x -2 y+6 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.178 |
|
| \begin{align*}
y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.026 |
|
| \begin{align*}
y^{\prime }&=\tan \left (y\right ) \\
\end{align*} | [_quadrature] | ✓ | ✓ | ✓ | ✓ | 1.231 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.918 |
|
| \begin{align*}
y^{\prime }&=\frac {6 x^{2}+4}{3 y^{2}-4 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.208 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.786 |
|
| \begin{align*}
\left (y^{2}-1\right ) y^{\prime }&=4 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.904 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{-y}+1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| \begin{align*}
y^{\prime }&=3 x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.744 |
|
| \begin{align*}
y^{\prime }&=\frac {2+\sqrt {x}}{2+\sqrt {y}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.701 |
|
| \begin{align*}
y^{\prime }-3 y^{2} x^{2}&=-3 x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.448 |
|
| \begin{align*}
y^{\prime }-3 y^{2} x^{2}&=3 x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.313 |
|
| \begin{align*}
y^{\prime }&=200 y-2 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
y^{\prime }-2 y&=-10 \\
y \left (0\right ) &= 8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
y^{\prime } y&=\sin \left (x \right ) \\
y \left (0\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.493 |
|
| \begin{align*}
y^{\prime }&=2 x -1+2 y x -y \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.341 |
|
| \begin{align*}
y^{\prime } x&=y^{2}-y \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.201 |
|
| \begin{align*}
y^{\prime } x&=y^{2}-y \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
3.202 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}-1}{y x} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.319 |
|
| \begin{align*}
\left (y^{2}-1\right ) y^{\prime }&=4 y x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
1.717 |
|
| \begin{align*}
x^{2} y^{\prime }+3 x^{2} y&=\sin \left (x \right ) \\
\end{align*} | [[_linear, ‘class A‘]] | ✓ | ✓ | ✓ | ✓ | 2.074 |
|
| \begin{align*}
y^{2} y^{\prime }+3 x^{2} y&=\sin \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
2.783 |
|
| \begin{align*}
y^{\prime }-x y^{2}&=\sqrt {x} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
0.250 |
|
| \begin{align*}
y^{\prime }&=1+\left (y x +3 y\right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
0.977 |
|
| \begin{align*}
y^{\prime }&=1+y x +3 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.329 |
|
| \begin{align*}
y^{\prime }&=4 y+8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
y^{\prime }-{\mathrm e}^{2 x}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.202 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.843 |
|
| \begin{align*}
y^{\prime }+4 y&=y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.739 |
|
| \begin{align*}
y^{\prime } x +\cos \left (x^{2}\right )&=827 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
23.283 |
|
| \begin{align*}
2 y+y^{\prime }&=6 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
2 y+y^{\prime }&=20 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| \begin{align*}
y^{\prime }&=4 y+16 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
y^{\prime }-2 y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.566 |
|
| \begin{align*}
y^{\prime } x +3 y-10 x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.923 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=\sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.796 |
|
| \begin{align*}
y^{\prime } x&=\sqrt {x}+3 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.233 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=\cos \left (x \right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.437 |
|
| \begin{align*}
y^{\prime } x +\left (2+5 x \right ) y&=\frac {20}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| \begin{align*}
2 \sqrt {x}\, y^{\prime }+y&=2 x \,{\mathrm e}^{-\sqrt {x}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.843 |
|
| \begin{align*}
y^{\prime }-3 y&=6 \\
y \left (0\right ) &= 5 \\
\end{align*} | [_quadrature] | ✓ | ✓ | ✓ | ✓ | 0.583 |
|
| \begin{align*}
y^{\prime }-3 y&=6 \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
y^{\prime }+5 y&={\mathrm e}^{-3 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.181 |
|
| \begin{align*}
y^{\prime } x +3 y&=20 x^{2} \\
y \left (1\right ) &= 10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.374 |
|
| \begin{align*}
y^{\prime } x&=y+x^{2} \cos \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.187 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \left (3+3 x^{2}-y\right ) \\
y \left (2\right ) &= 8 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.632 |
|
| \begin{align*}
y^{\prime }+6 y x&=\sin \left (x \right ) \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.032 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=\sqrt {x}\, \sin \left (x \right ) \\
y \left (2\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.681 |
|
| \begin{align*}
-y+y^{\prime } x&=x^{2} {\mathrm e}^{-x^{2}} \\
y \left (3\right ) &= 8 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.209 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\left (3 x +3 y+2\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.794 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (3 x -2 y\right )^{2}+1}{3 x -2 y}+\frac {3}{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.302 |
|
| \begin{align*}
\cos \left (-4 y+8 x -3\right ) y^{\prime }&=2+2 \cos \left (-4 y+8 x -3\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.483 |
|
| \begin{align*}
y^{\prime }&=1+\left (y-x \right )^{2} \\
y \left (0\right ) &= {\frac {1}{4}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.362 |
|
| \begin{align*}
x^{2} y^{\prime }-y x&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.497 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.193 |
|
| \begin{align*}
\cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right )&=1+\sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.030 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
y \left (0\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.046 |
|
| \begin{align*}
y^{\prime }+3 y&=3 y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=\frac {y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.894 |
|
| \begin{align*}
y^{\prime }+3 \cot \left (x \right ) y&=6 \cos \left (x \right ) y^{{2}/{3}} \\
\end{align*} | [_Bernoulli] | ✓ | ✓ | ✓ | ✓ | 4.906 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=\frac {1}{y} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.756 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\frac {x^{2}}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.750 |
|
| \begin{align*}
3 y^{\prime }&=-2+\sqrt {2 x +3 y+4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.280 |
|
| \begin{align*}
3 y^{\prime }+\frac {2 y}{x}&=4 \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.272 |
|
| \begin{align*}
y^{\prime }&=4+\frac {1}{\sin \left (4 x -y\right )} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.664 |
|