Link to actual problem [9317] \[ \boxed {y^{\prime }-\frac {y \left (x^{2} y^{2}+y x \,{\mathrm e}^{x}+{\mathrm e}^{2 x}\right ) {\mathrm e}^{-2 x} \left (x -1\right )}{x}=0} \]
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 {x}{-1+x}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \\ \end{align*}