| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=x +\frac {y^{2}}{2} \\
y \left (-2\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
2.842 |
|
| \begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
39.950 |
|
| \begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
8.754 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
4.909 |
|
| \begin{align*}
y^{\prime }&=t +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
23.086 |
|
| \begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
12.201 |
|
| \begin{align*}
y^{\prime }&=t +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
18.077 |
|
| \begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
6.652 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
5.334 |
|
| \begin{align*}
y^{\prime }&=a x +b y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
35.309 |
|
| \begin{align*}
y^{\prime }&=a \,x^{n}+b y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
33.747 |
|
| \begin{align*}
y^{\prime } x +a +x y^{2}&=0 \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
2.513 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b \,x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
6.015 |
|
| \begin{align*}
x^{{3}/{2}} y^{\prime }&=a +b \,x^{{3}/{2}} y^{2} \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
0.138 |
|
| \begin{align*}
y^{\prime }+y^{2}&=\frac {a^{2}}{x^{4}} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.635 |
|
| \begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
10.593 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
7.159 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (3\right ) &= 0 \\
\end{align*} | [_Riccati] | ✓ | ✓ | ✓ | ✗ | 5.687 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
4.168 |
|
| \begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
36.454 |
|
| \begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
41.976 |
|
| \begin{align*}
y^{\prime }&=a x +b y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
38.549 |
|
| \begin{align*}
c y^{\prime }&=a x +b y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
35.672 |
|
| \begin{align*}
c y^{\prime }&=\frac {a x +b y^{2}}{r} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
3.052 |
|
| \begin{align*}
y^{\prime }&=x -y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
6.756 |
|
| \begin{align*}
y^{\prime }+y^{2}+a \,x^{m}&=0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
31.501 |
|
| \begin{align*}
y^{\prime }+a y^{2}-b \,x^{\nu }&=0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
32.036 |
|
| \begin{align*}
y^{\prime } x +a +x y^{2}&=0 \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
2.796 |
|
| \begin{align*}
x^{2} \left (y^{\prime }+a y^{2}\right )-b&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
3.454 |
|
| \begin{align*}
x^{4} \left (y^{\prime }+y^{2}\right )+a&=0 \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
3.875 |
|
| \begin{align*}
y^{\prime }&=a y^{2}+b \,x^{n} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
40.608 |
|
| \begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}+b \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
4.262 |
|
| \begin{align*}
x^{\prime }&=t^{2}+x^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
39.881 |
|
| \begin{align*}
x^{\prime }&=t -x^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
4.858 |
|
| \begin{align*}
y^{\prime }&=x +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
17.819 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
5.105 |
|
| \begin{align*}
y^{\prime }&=x -y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} | [[_Riccati, _special]] | ✓ | ✓ | ✓ | ✗ | 20.332 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
5.023 |
|
| \begin{align*}
y^{\prime }&=y^{2}-x^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
4.477 |
|
| \begin{align*}
y^{\prime }-y^{2}&=x \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
2.532 |
|
| \begin{align*}
y^{\prime }+t^{2}&=y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
8.667 |
|
| \begin{align*}
y^{\prime }&=y^{2}-x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
22.806 |
|
| \begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
45.764 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
7.887 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
8.106 |
|
| \begin{align*}
y^{\prime }&=x +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
128.487 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{3}+\frac {2}{3 x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
2.378 |
|
| \begin{align*}
y^{\prime }&=y^{2}+\frac {1}{x^{4}} \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
3.029 |
|
| \begin{align*}
y^{\prime }&=y^{2}-x^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
6.468 |
|
| \begin{align*}
x^{\prime }&=t +x^{2} \\
x \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
24.842 |
|
| \begin{align*}
x^{\prime }&=x^{2}-t^{2} \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
12.723 |
|
| \begin{align*}
y^{\prime }&=x +y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
2.126 |
|
| \begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
43.588 |
|
| \begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
37.593 |
|
| \begin{align*}
y^{\prime }&=t +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
25.266 |
|
| \begin{align*}
y^{\prime }&=y^{2}-t \\
\end{align*} | [[_Riccati, _special]] | ✓ | ✓ | ✓ | ✗ | 2.280 |
|
| \begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
13.135 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
7.864 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (3\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
6.389 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
5.192 |
|