Link to actual problem [9310] \[ \boxed {y^{\prime }-y \left (y^{2}+{\mathrm e}^{-x^{2}} y+{\mathrm e}^{-2 x^{2}}\right ) {\mathrm e}^{2 x^{2}} x=0} \]
type detected by program
{"abelFirstKind"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(y)]`], _Abel]
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 &= -\frac {1}{2 x}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \\ \end{align*}