Link to actual problem [8652] \[ \boxed {\left (2 y^{3} x +y\right ) y^{\prime }+2 y^{2}=0} \]
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[_rational, [_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*}