| # |
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]] |
✓ |
✓ |
✓ |
✗ |
0.421 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
6.339 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
8.335 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
4.672 |
|
| \begin{align*}
y^{\prime }&=t +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
30.233 |
|
| \begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
17.093 |
|
| \begin{align*}
y^{\prime }&=t +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
9.888 |
|
| \begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
16.779 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
8.440 |
|
| \begin{align*}
y^{\prime }&=a x +b y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
30.832 |
|
| \begin{align*}
y^{\prime }&=a \,x^{n}+b y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
36.770 |
|
| \begin{align*}
x y^{\prime }+a +x y^{2}&=0 \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
6.516 |
|
| \begin{align*}
x^{2} y^{\prime }&=a +b \,x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
7.020 |
|
| \begin{align*}
x^{4} y^{\prime }+a^{2}+y^{2} x^{4}&=0 \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
8.767 |
|
| \begin{align*}
x^{{3}/{2}} y^{\prime }&=a +b \,x^{{3}/{2}} y^{2} \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
0.310 |
|
| \begin{align*}
y^{\prime }+y^{2}&=\frac {a^{2}}{x^{4}} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.275 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
10.951 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
8.598 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (3\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
7.500 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
6.140 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
7.417 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
6.247 |
|
| \begin{align*}
y^{\prime }&=a x +b y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
29.630 |
|
| \begin{align*}
c y^{\prime }&=a x +b y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
28.050 |
|
| \begin{align*}
c y^{\prime }&=\frac {a x +b y^{2}}{r} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
4.136 |
|
| \begin{align*}
y^{\prime }&=x -y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
4.655 |
|
| \begin{align*}
y^{\prime }+y^{2}+a \,x^{m}&=0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
29.387 |
|
| \begin{align*}
y^{\prime }+a y^{2}-b \,x^{\nu }&=0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
29.213 |
|
| \begin{align*}
x y^{\prime }+a +x y^{2}&=0 \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
2.783 |
|
| \begin{align*}
x^{2} \left (y^{\prime }+a y^{2}\right )-b&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
4.205 |
|
| \begin{align*}
x^{4} \left (y^{\prime }+y^{2}\right )+a&=0 \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
5.105 |
|
| \begin{align*}
y^{\prime }&=a y^{2}+b \,x^{n} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
33.462 |
|
| \begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}+b \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
5.169 |
|
| \begin{align*}
x^{4} y^{\prime }&=-y^{2} x^{4}-a^{2} \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
5.822 |
|
| \begin{align*}
x^{\prime }&=t^{2}+x^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
14.314 |
|
| \begin{align*}
x^{\prime }&=t -x^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
8.874 |
|
| \begin{align*}
y^{\prime }&=x +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
34.610 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
13.478 |
|
| \begin{align*}
y^{\prime }&=x -y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
313.578 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
12.984 |
|
| \begin{align*}
y^{\prime }&=y^{2}-x^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
12.688 |
|
| \begin{align*}
y^{\prime }-y^{2}&=x \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
4.003 |
|
| \begin{align*}
y^{\prime }+t^{2}&=y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
8.862 |
|
| \begin{align*}
y^{\prime }&=y^{2}-x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
22.181 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
12.220 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
9.165 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
9.558 |
|
| \begin{align*}
y^{\prime }&=x +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
280.695 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{3}+\frac {2}{3 x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
3.444 |
|
| \begin{align*}
y^{\prime }&=y^{2}+\frac {1}{x^{4}} \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
4.039 |
|
| \begin{align*}
y^{\prime }&=y^{2}-x^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
5.041 |
|
| \begin{align*}
x^{\prime }&=t +x^{2} \\
x \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
26.705 |
|
| \begin{align*}
x^{\prime }&=x^{2}-t^{2} \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
9.850 |
|
| \begin{align*}
y^{\prime }&=x +y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
8.059 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
9.046 |
|
| \begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
9.967 |
|
| \begin{align*}
y^{\prime }&=t +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
274.027 |
|
| \begin{align*}
y^{\prime }&=y^{2}-t \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
8.634 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
17.770 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
14.046 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (3\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
13.003 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
11.827 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
6.471 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
4.671 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
7.013 |
|
| \begin{align*}
y^{\prime }&=y^{2}-\frac {2}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
5.911 |
|
| \begin{align*}
3 y^{\prime }+y^{2}+\frac {2}{x^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
3.141 |
|
| \begin{align*}
y^{\prime }&=x -y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
3.043 |
|