Link to actual problem [8422] \[ \boxed {y^{\prime }-x^{-1+a} y^{1-b} f \left (\frac {x^{a}}{a}+\frac {y^{b}}{b}\right )=0} \]
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 [R &= \frac {x^{a} b +y^{b} a}{a}, S \left (R \right ) &= \frac {x^{a}}{a}\right ] \\ \end{align*}