Link to actual problem [9137] \[ \boxed {y^{\prime }-\frac {f_{1} \left (y^{2}-2 \ln \left (x \right )\right )}{\sqrt {y^{2}}\, x}=0} \]
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 &= x, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{y}\right ] \\ \\ \end{align*}