Link to actual problem [8929] \[ \boxed {y^{\prime }-\frac {F \left (\frac {y^{2} x +1}{x}\right )}{y x^{2}}=0} \]
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 &= 2 x^{2}, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{y}\right ] \\ \left [R &= \frac {1+x y^{2}}{x}, S \left (R \right ) &= -\frac {1}{2 x}\right ] \\ \end{align*}