Link to actual problem [13460] \[ \boxed {y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }=-x} \]
type detected by program
{"exact"}
type detected by Maple
[_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
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 {{\mathrm e}^{-x y}}{x}\right ] \\ \\ \end{align*}