Link to actual problem [8456] \[ \boxed {x y^{\prime }-y \left (x \ln \left (\frac {x^{2}}{y}\right )+2\right )=0} \]
type detected by program
{"unknown"}
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 &= 1, \underline {\hspace {1.25 ex}}\eta &= \frac {2 y}{x}\right ] \\ \left [R &= \frac {y}{x^{2}}, S \left (R \right ) &= x\right ] \\ \end{align*}