| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=2 x +1 \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
y^{\prime }&=\left (x -2\right )^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.309 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x} \\
y \left (4\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.582 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}} \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\sqrt {2+x}} \\
y \left (2\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.285 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {x^{2}+9} \\
y \left (-4\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
y^{\prime }&=\frac {10}{x^{2}+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \begin{align*}
y^{\prime }&=\cos \left (2 x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.311 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{-x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.291 |
|
| \begin{align*}
x^{\prime \prime }&=50 \\
x \left (0\right ) &= 20 \\
x^{\prime }\left (0\right ) &= 10 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.683 |
|
| \begin{align*}
x^{\prime \prime }&=-20 \\
x \left (0\right ) &= 5 \\
x^{\prime }\left (0\right ) &= -15 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| \begin{align*}
x^{\prime \prime }&=3 t \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| \begin{align*}
x^{\prime \prime }&=2 t +1 \\
x \left (0\right ) &= 4 \\
x^{\prime }\left (0\right ) &= -7 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.687 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.697 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.789 |
|
| \begin{align*}
x^{\prime \prime }&=\frac {1}{\left (1+t \right )^{3}} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.822 |
|
| \begin{align*}
y^{\prime }&=-y-\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.588 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.737 |
|
| \begin{align*}
y^{\prime }&=y-\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.592 |
|
| \begin{align*}
y^{\prime }&=x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.858 |
|
| \begin{align*}
y^{\prime }&=y-x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| \begin{align*}
y^{\prime }&=x -y+1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.989 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.446 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y-2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| \begin{align*}
y^{\prime }&=2 y^{2} x^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.944 |
|
| \begin{align*}
y^{\prime }&=\ln \left (y\right ) x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.195 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.813 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
38.704 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x -y} \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✓ |
1.805 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x -y} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.526 |
|
| \begin{align*}
y y^{\prime }&=x -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.782 |
|
| \begin{align*}
y y^{\prime }&=x -1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.782 |
|
| \begin{align*}
y^{\prime }&=\ln \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.967 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Riccati] |
✗ |
✓ |
✓ |
✗ |
7.138 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.749 |
|
| \begin{align*}
y^{\prime }&=-x +y \\
y \left (4\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2}-1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✓ |
✗ |
26.394 |
|
| \begin{align*}
y^{\prime }&=x +\frac {y^{2}}{2} \\
y \left (-2\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
0.270 |
|
| \begin{align*}
y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.654 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.502 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.885 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=4 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.941 |
|
| \begin{align*}
2 \sqrt {x}\, y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.039 |
|
| \begin{align*}
y^{\prime }&=3 \sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \begin{align*}
y^{\prime }&=64^{{1}/{3}} \left (y x \right )^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
0.230 |
|
| \begin{align*}
y^{\prime }&=2 x \sec \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.888 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime }&=\left (1+y\right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.845 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.036 |
|
| \begin{align*}
y y^{\prime }&=x \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.763 |
|
| \begin{align*}
y^{3} y^{\prime }&=\left (1+y^{4}\right ) \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.412 |
|
| \begin{align*}
y^{\prime }&=\frac {1+\sqrt {x}}{1+\sqrt {y}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.108 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.303 |
|
| \begin{align*}
\left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime }&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.055 |
|
| \begin{align*}
y^{\prime }&=1+x +y+y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.562 |
|
| \begin{align*}
x^{2} y^{\prime }&=1-x^{2}+y^{2}-y^{2} x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.805 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x} y \\
y \left (0\right ) &= 2 \,{\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| \begin{align*}
y^{\prime }&=3 x^{2} \left (1+y^{2}\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.681 |
|
| \begin{align*}
2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\
y \left (5\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.681 |
|
| \begin{align*}
y^{\prime }&=4 x^{3} y-y \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.055 |
|
| \begin{align*}
1+y^{\prime }&=2 y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
\tan \left (x \right ) y^{\prime }&=y \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.252 |
|
| \begin{align*}
-y+y^{\prime } x&=2 x^{2} y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.757 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2}+3 y^{2} x^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.510 |
|
| \begin{align*}
y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.743 |
|
| \begin{align*}
2 \sqrt {x}\, y^{\prime }&=\cos \left (y\right )^{2} \\
y \left (4\right ) &= \frac {\pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.082 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (a \right ) &= b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.273 |
|
| \begin{align*}
{y^{\prime }}^{2}&=4 y \\
y \left (a \right ) &= b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.839 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (a \right ) &= b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.188 |
|
| \begin{align*}
y^{\prime }&=y \sqrt {-1+y^{2}} \\
y \left (a \right ) &= b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.961 |
|
| \begin{align*}
y^{\prime }+y&=2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \begin{align*}
y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.160 |
|
| \begin{align*}
y^{\prime }+3 y&=2 x \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.945 |
|
| \begin{align*}
y^{\prime }-2 y x&={\mathrm e}^{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.822 |
|
| \begin{align*}
y^{\prime } x +2 y&=3 x \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.230 |
|
| \begin{align*}
y^{\prime } x +5 y&=7 x^{2} \\
y \left (2\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.094 |
|
| \begin{align*}
2 y^{\prime } x +y&=10 \sqrt {x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.093 |
|
| \begin{align*}
y+3 y^{\prime } x&=12 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.329 |
|
| \begin{align*}
-y+y^{\prime } x&=x \\
y \left (1\right ) &= 7 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.730 |
|
| \begin{align*}
2 y^{\prime } x -3 y&=9 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.770 |
|
| \begin{align*}
y^{\prime } x +y&=3 y x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.596 |
|
| \begin{align*}
y^{\prime } x +3 y&=2 x^{5} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.098 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.101 |
|
| \begin{align*}
y^{\prime } x -3 y&=x^{3} \\
y \left (1\right ) &= 10 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.527 |
|
| \begin{align*}
y^{\prime }+2 y x&=x \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| \begin{align*}
y^{\prime }&=\left (1-y\right ) \cos \left (x \right ) \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.986 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y&=\cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.733 |
|
| \begin{align*}
y^{\prime } x&=2 y+x^{3} \cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.063 |
|
| \begin{align*}
y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.766 |
|
| \begin{align*}
y^{\prime }&=1+x +y+y x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.664 |
|
| \begin{align*}
y^{\prime } x&=3 y+x^{4} \cos \left (x \right ) \\
y \left (2 \pi \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.347 |
|
| \begin{align*}
y^{\prime }&=2 y x +3 x^{2} {\mathrm e}^{x^{2}} \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.206 |
|
| \begin{align*}
y^{\prime } x +\left (2 x -3\right ) y&=4 x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| \begin{align*}
\left (x^{2}+4\right ) y^{\prime }+3 y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.885 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
3.072 |
|
| \begin{align*}
\frac {1-4 x y^{2}}{x^{\prime }}&=y^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.884 |
|
| \begin{align*}
\frac {x+y \,{\mathrm e}^{y}}{x^{\prime }}&=1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.636 |
|
| \begin{align*}
\frac {1+2 x y}{x^{\prime }}&=y^{2}+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.500 |
|