Link to actual problem [15037] \[ \boxed {\left (\frac {{\mathrm e}^{-y^{2}}}{2}-y x \right ) y^{\prime }=1} \]
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 &= {\mathrm e}^{-\frac {y^{2}}{2}}, \underline {\hspace {1.25 ex}}\eta &= 0\right ] \\ \left [R &= y, S \left (R \right ) &= {\mathrm e}^{\frac {y^{2}}{2}} x\right ] \\ \end{align*}