| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=2 x +1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
y^{\prime }&=\left (x -2\right )^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.311 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x} \\
y \left (4\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}} \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\sqrt {2+x}} \\
y \left (2\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.280 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {x^{2}+9} \\
y \left (-4\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.464 |
|
| \begin{align*}
y^{\prime }&=\frac {10}{x^{2}+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.251 |
|
| \begin{align*}
y^{\prime }&=\cos \left (2 x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.357 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.264 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{-x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.253 |
|
| \begin{align*}
x^{\prime \prime }&=50 \\
x \left (0\right ) &= 20 \\
x^{\prime }\left (0\right ) &= 10 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \begin{align*}
x^{\prime \prime }&=-20 \\
x \left (0\right ) &= 5 \\
x^{\prime }\left (0\right ) &= -15 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.741 |
|
| \begin{align*}
x^{\prime \prime }&=3 t \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.813 |
|
| \begin{align*}
x^{\prime \prime }&=2 t +1 \\
x \left (0\right ) &= 4 \\
x^{\prime }\left (0\right ) &= -7 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| \begin{align*}
x^{\prime \prime }&=4 \left (t +3\right )^{2} \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.827 |
|
| \begin{align*}
x^{\prime \prime }&=\frac {1}{\sqrt {t +4}} \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.925 |
|
| \begin{align*}
x^{\prime \prime }&=\frac {1}{\left (t +1\right )^{3}} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.909 |
|
| \begin{align*}
x^{\prime \prime }&=50 \sin \left (5 t \right ) \\
x \left (0\right ) &= 8 \\
x^{\prime }\left (0\right ) &= -10 \\
\end{align*} | [[_2nd_order, _quadrature]] | ✓ | ✓ | ✓ | ✓ | 1.953 |
|
| \begin{align*}
y^{\prime }&=-y-\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.274 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| \begin{align*}
y^{\prime }&=y-\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.256 |
|
| \begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| \begin{align*}
y^{\prime }&=y-x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| \begin{align*}
y^{\prime }&=x -y+1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.187 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y-2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.221 |
|
| \begin{align*}
y^{\prime }&=2 y^{2} x^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.416 |
|
| \begin{align*}
y^{\prime }&=\ln \left (y\right ) x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
1.864 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.834 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.503 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x -y} \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✓ |
3.451 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x -y} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.250 |
|
| \begin{align*}
y^{\prime } y&=x -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.164 |
|
| \begin{align*}
y^{\prime } y&=x -1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.980 |
|
| \begin{align*}
y^{\prime }&=\ln \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.362 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Riccati] |
✗ |
✓ |
✓ |
✗ |
5.764 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 0 \\
\end{align*} | [[_linear, ‘class A‘]] | ✓ | ✓ | ✓ | ✓ | 0.844 |
|
| \begin{align*}
y^{\prime }&=y-x \\
y \left (4\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.892 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2}-1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✓ |
✗ |
44.348 |
|
| \begin{align*}
y^{\prime }&=x +\frac {y^{2}}{2} \\
y \left (-2\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
2.842 |
|
| \begin{align*}
y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.985 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.858 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.338 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=4 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.520 |
|
| \begin{align*}
2 \sqrt {x}\, y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.340 |
|
| \begin{align*}
y^{\prime }&=3 \sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
10.072 |
|
| \begin{align*}
y^{\prime }&=64^{{1}/{3}} \left (y x \right )^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
59.928 |
|
| \begin{align*}
y^{\prime }&=2 x \sec \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.812 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.177 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime }&=\left (1+y\right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.480 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.207 |
|
| \begin{align*}
y^{\prime } y&=x \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.450 |
|
| \begin{align*}
y^{3} y^{\prime }&=\left (1+y^{4}\right ) \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.907 |
|
| \begin{align*}
y^{\prime }&=\frac {1+\sqrt {x}}{1+\sqrt {y}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.345 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.622 |
|
| \begin{align*}
\left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime }&=x \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 2.155 |
|
| \begin{align*}
y^{\prime }&=1+x +y+y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.371 |
|
| \begin{align*}
x^{2} y^{\prime }&=1-x^{2}+y^{2}-y^{2} x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.529 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x} y \\
y \left (0\right ) &= 2 \,{\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.670 |
|
| \begin{align*}
y^{\prime }&=3 x^{2} \left (1+y^{2}\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.790 |
|
| \begin{align*}
2 y^{\prime } y&=\frac {x}{\sqrt {x^{2}-16}} \\
y \left (5\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.478 |
|
| \begin{align*}
y^{\prime }&=4 x^{3} y-y \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.086 |
|
| \begin{align*}
1+y^{\prime }&=2 y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \begin{align*}
\tan \left (x \right ) y^{\prime }&=y \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.716 |
|
| \begin{align*}
-y+y^{\prime } x&=2 x^{2} y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.590 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2}+3 y^{2} x^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.297 |
|
| \begin{align*}
y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.580 |
|
| \begin{align*}
2 \sqrt {x}\, y^{\prime }&=\cos \left (y\right )^{2} \\
y \left (4\right ) &= \frac {\pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.507 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (a \right ) &= b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.192 |
|
| \begin{align*}
{y^{\prime }}^{2}&=4 y \\
y \left (a \right ) &= b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.773 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (a \right ) &= b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.091 |
|
| \begin{align*}
y^{\prime }&=y \sqrt {y^{2}-1} \\
y \left (a \right ) &= b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
40.859 |
|
| \begin{align*}
y^{\prime }+y&=2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.964 |
|
| \begin{align*}
y^{\prime }+3 y&=2 x \,{\mathrm e}^{-3 x} \\
\end{align*} | [[_linear, ‘class A‘]] | ✓ | ✓ | ✓ | ✓ | 2.355 |
|
| \begin{align*}
y^{\prime }-2 y x&={\mathrm e}^{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.749 |
|
| \begin{align*}
y^{\prime } x +2 y&=3 x \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.947 |
|
| \begin{align*}
y^{\prime } x +5 y&=7 x^{2} \\
y \left (2\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.072 |
|
| \begin{align*}
2 y^{\prime } x +y&=10 \sqrt {x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| \begin{align*}
y+3 y^{\prime } x&=12 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.042 |
|
| \begin{align*}
-y+y^{\prime } x&=x \\
y \left (1\right ) &= 7 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.819 |
|
| \begin{align*}
2 y^{\prime } x -3 y&=9 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.638 |
|
| \begin{align*}
y^{\prime } x +y&=3 y x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.482 |
|
| \begin{align*}
y^{\prime } x +3 y&=2 x^{5} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.048 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.969 |
|
| \begin{align*}
y^{\prime } x -3 y&=x^{3} \\
y \left (1\right ) &= 10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.423 |
|
| \begin{align*}
y^{\prime }&=\left (1-y\right ) \cos \left (x \right ) \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.884 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y&=\cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.662 |
|
| \begin{align*}
y^{\prime } x&=2 y+\cos \left (x \right ) x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.462 |
|
| \begin{align*}
y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.519 |
|
| \begin{align*}
y^{\prime }&=1+x +y+y x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.450 |
|
| \begin{align*}
y^{\prime } x&=3 y+x^{4} \cos \left (x \right ) \\
y \left (2 \pi \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.207 |
|
| \begin{align*}
y^{\prime }&=2 y x +3 x^{2} {\mathrm e}^{x^{2}} \\
y \left (0\right ) &= 5 \\
\end{align*} | [_linear] | ✓ | ✓ | ✓ | ✓ | 3.101 |
|
| \begin{align*}
y^{\prime } x +\left (2 x -3\right ) y&=4 x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| \begin{align*}
\left (x^{2}+4\right ) y^{\prime }+3 y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.793 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+3 x^{3} y&=6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
1.939 |
|
| \begin{align*}
\frac {1-4 x y^{2}}{x^{\prime }}&=y^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.500 |
|
| \begin{align*}
\frac {x+y \,{\mathrm e}^{y}}{x^{\prime }}&=1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.554 |
|
| \begin{align*}
\frac {1+2 x y}{x^{\prime }}&=y^{2}+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.425 |
|