Link to actual problem [6232] \[ \boxed {y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime }=0} \]
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[[_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 &= \frac {1}{y^{2}}, \underline {\hspace {1.25 ex}}\eta &= 0\right ] \\ \\ \end{align*}