| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=-2 x \left (y^{3}-3 y+2\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.504 |
|
| \begin{align*}
y^{\prime }&=a \,x^{\frac {n}{1-n}}+b y^{n} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
12.842 |
|
| \begin{align*}
-a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
6.204 |
|
| \begin{align*}
-a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
6.121 |
|
| \begin{align*}
y^{\prime }-a y^{n}-b \,x^{\frac {n}{1-n}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
4.417 |
|
| \begin{align*}
y^{\prime }-f \left (x \right )^{1-n} g^{\prime }\left (x \right ) y^{n} \left (a g \left (x \right )+b \right )^{-n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right )&=0 \\
\end{align*} |
[_Chini, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.976 |
|
| \begin{align*}
y^{\prime }-a^{n} f \left (x \right )^{1-n} g^{\prime }\left (x \right ) y^{n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right )&=0 \\
\end{align*} |
[_Chini, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.413 |
|
| \begin{align*}
x^{1+2 n} y^{\prime }-a y^{3}-b \,x^{3 n}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
10.158 |
|
| \begin{align*}
x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (m +1\right )}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
6.694 |
|
| \begin{align*}
y^{\prime }&=a y^{3}+\frac {b}{x^{{3}/{2}}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
16.392 |
|
| \begin{align*}
y^{\prime }&=a \,x^{1+2 n} y^{3}+b \,x^{-n -2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
21.765 |
|
| \begin{align*}
y^{\prime }&=-\frac {{\mathrm e}^{2 \lambda x} y^{3}}{3 \lambda }+\frac {2 \lambda ^{2} {\mathrm e}^{-\lambda x}}{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
9.835 |
|