| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.413 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.487 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\
y \left (3\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.317 |
|
| \begin{align*}
y^{\prime }&=\cos \left (y\right ) \sin \left (x \right ) \\
y \left (0\right ) &= -{\frac {5}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.561 |
|
| \begin{align*}
y^{\prime }&=x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.874 |
|
| \begin{align*}
y^{\prime }&=x \\
y \left (0\right ) &= -3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (-2\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.885 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (1\right ) &= -3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.475 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.704 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.092 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y} \\
y \left (-2\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.872 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{5}+y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.569 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{5}+y \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.414 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.612 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{y} \\
y \left (1\right ) &= {\frac {5}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.022 |
|
| \begin{align*}
y^{\prime }&=y-\cos \left (\frac {\pi x}{2}\right ) \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.158 |
|
| \begin{align*}
y^{\prime }&=y-\cos \left (\frac {\pi x}{2}\right ) \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.579 |
|
| \begin{align*}
y^{\prime }&=1-\frac {y}{x} \\
y \left (-\frac {1}{2}\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.483 |
|
| \begin{align*}
y^{\prime }&=1-\frac {y}{x} \\
y \left (\frac {3}{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.277 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.626 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
5.759 |
|
| \begin{align*}
y^{\prime }&=x \left (y-4\right )^{2}-2 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
79.758 |
|
| \begin{align*}
y^{\prime }&=x^{2}-2 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.571 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.351 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y^{4} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| \begin{align*}
y^{\prime }&=y^{2}-3 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.600 |
|
| \begin{align*}
y^{\prime }&=\left (-2+y\right )^{4} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| \begin{align*}
y^{\prime }&=10+3 y-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \begin{align*}
y^{\prime }&=y^{2} \left (4-y^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| \begin{align*}
y^{\prime }&=y \left (2-y\right ) \left (4-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.109 |
|
| \begin{align*}
y^{\prime }&=y \ln \left (y+2\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.197 |
|
| \begin{align*}
y^{\prime }&=\left ({\mathrm e}^{y} y-9 y\right ) {\mathrm e}^{-y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.437 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{\pi }-\sin \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.315 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y-6 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \begin{align*}
m v^{\prime }&=m g -k v^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.462 |
|
| \begin{align*}
y^{\prime }&=\sin \left (5 x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| \begin{align*}
y^{\prime }&=\left (x +1\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.287 |
|
| \begin{align*}
1+{\mathrm e}^{3 x} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| \begin{align*}
y^{\prime }-\left (-1+y\right )^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.403 |
|
| \begin{align*}
y^{\prime } x&=4 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.007 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.389 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 x +2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.625 |
|
| \begin{align*}
y \,{\mathrm e}^{x} y^{\prime }&={\mathrm e}^{-y}+{\mathrm e}^{-2 x -y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.842 |
|
| \begin{align*}
y \ln \left (x \right ) y^{\prime }&=\frac {\left (1+y\right )^{2}}{x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.115 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (3+2 y\right )^{2}}{\left (5+4 x \right )^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.296 |
|
| \begin{align*}
\csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.376 |
|
| \begin{align*}
\sin \left (3 x \right )+2 y \cos \left (3 x \right )^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.794 |
|
| \begin{align*}
\left (1+{\mathrm e}^{y}\right )^{2} {\mathrm e}^{-y}+\left ({\mathrm e}^{x}+1\right )^{3} {\mathrm e}^{-x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.208 |
|
| \begin{align*}
x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.974 |
|
| \begin{align*}
s^{\prime }&=k s \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \begin{align*}
q^{\prime }&=k \left (q-70\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
p^{\prime }&=p-p^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.960 |
|
| \begin{align*}
n^{\prime }+n&=n t \,{\mathrm e}^{t +2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.546 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +3 x -y-3}{y x -2 x +4 y-8} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.043 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +2 y-x -2}{y x -3 y+x -3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.886 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {1-y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| \begin{align*}
\left ({\mathrm e}^{x}+{\mathrm e}^{-x}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.068 |
|
| \begin{align*}
x^{\prime }&=4 x^{2}+4 \\
x \left (\frac {\pi }{4}\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
22.622 |
|
| \begin{align*}
y^{\prime }&=\frac {-1+y^{2}}{x^{2}-1} \\
y \left (2\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
4.451 |
|
| \begin{align*}
x^{2} y^{\prime }&=y-y x \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| \begin{align*}
y^{\prime }+2 y&=1 \\
y \left (0\right ) &= {\frac {5}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| \begin{align*}
\sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\
y \left (0\right ) &= \frac {\sqrt {3}}{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
10.670 |
|
| \begin{align*}
\left (x^{4}+1\right ) y^{\prime }+x \left (1+4 y^{2}\right )&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
3.679 |
|
| \begin{align*}
y^{\prime }&=-y \ln \left (y\right ) \\
y \left (0\right ) &= {\mathrm e} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.264 |
|
| \begin{align*}
x \sinh \left (y\right ) y^{\prime }&=\cosh \left (y\right ) \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.473 |
|
| \begin{align*}
y^{\prime }&=y \,{\mathrm e}^{-x^{2}} \\
y \left (4\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.518 |
|
| \begin{align*}
y^{\prime }&=y^{2} \sin \left (x^{2}\right ) \\
y \left (-2\right ) &= {\frac {1}{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.197 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2}\right ) \sqrt {1+\cos \left (x^{3}\right )} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
11.806 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{-2 y} \sin \left (x \right )}{x^{2}+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.323 |
|
| \begin{align*}
y^{\prime }&=\frac {1+3 x}{2 y} \\
y \left (-2\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.964 |
|
| \begin{align*}
\left (-2+2 y\right ) y^{\prime }&=3 x^{2}+4 x +2 \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.487 |
|
| \begin{align*}
{\mathrm e}^{y}-{\mathrm e}^{-x} y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.179 |
|
| \begin{align*}
\sin \left (x \right )+y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.406 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.278 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.660 |
|
| \begin{align*}
y^{\prime }&=y^{2}-4 \\
y \left (\frac {1}{4}\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
12.332 |
|
| \begin{align*}
y^{\prime } x&=y^{2}-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.197 |
|
| \begin{align*}
y^{\prime } x&=y^{2}-y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.251 |
|
| \begin{align*}
y^{\prime } x&=y^{2}-y \\
y \left (\frac {1}{2}\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.234 |
|
| \begin{align*}
y^{\prime } x&=y^{2}-y \\
y \left (2\right ) &= {\frac {1}{4}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.230 |
|
| \begin{align*}
2 x \sin \left (y\right )^{2}-\left (x^{2}+10\right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.810 |
|
| \begin{align*}
y^{\prime }&=\left (-1+y\right )^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.293 |
|
| \begin{align*}
y^{\prime }&=\left (-1+y\right )^{2} \\
y \left (0\right ) &= {\frac {101}{100}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.458 |
|
| \begin{align*}
y^{\prime }&=\left (-1+y\right )^{2}+\frac {1}{100} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.773 |
|
| \begin{align*}
y^{\prime }&=\left (-1+y\right )^{2}-\frac {1}{100} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
2.312 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
3.121 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
3.224 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.004 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
6.928 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y-3} \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y-3} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y-3} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y-3} \\
y \left (-1\right ) &= 4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{1+\sin \left (x \right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
y^{\prime }&=\frac {\sin \left (\sqrt {x}\right )}{\sqrt {y}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.224 |
|
| \begin{align*}
\left (\sqrt {x}+x \right ) y^{\prime }&=\sqrt {y}+y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.786 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{3}}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
50.940 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{\sqrt {x}}}{y} \\
y \left (1\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.994 |
|