Link to actual problem [8681] \[ \boxed {x \left (2 x^{2} y \ln \left (y\right )+1\right ) y^{\prime }-2 y=0} \]
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 {x^{3}}{y}, \underline {\hspace {1.25 ex}}\eta &= 0\right ] \\ \left [R &= y, S \left (R \right ) &= -\frac {y}{2 x^{2}}\right ] \\ \end{align*}