Link to actual problem [2716] \[ \boxed {2 x \,{\mathrm e}^{y}+\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime }=0} \]
type detected by program
{"exact"}
type detected by Maple
[_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
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}{3 y^{2}+x^{2} {\mathrm e}^{y}}\right ] \\ \\ \end{align*}