Link to actual problem [8949] \[ \boxed {y^{\prime }-\frac {y}{x \left (-1+F \left (x y\right ) y\right )}=0} \]
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(y)]`]]
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}{y}, \underline {\hspace {1.25 ex}}\eta &= 1\right ] \\ \\ \end{align*}