Link to actual problem [3168] \[ \boxed {3 y \left (x^{2}-1\right )+\left (x^{3}+8 y-3 x \right ) y^{\prime }=0} \]
type detected by program
{"exact", "differentialType"}
type detected by Maple
[_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class A`]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\).\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{x^{3}-3 x +8 y}\right ] \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {y \left (x^{3}-3 x +4 y \right )}{x^{3}-3 x +8 y}\right ] \\ \\ \end{align*}