Link to actual problem [8922] \[ \boxed {y^{\prime }-\frac {x +F \left (-\left (x -y\right ) \left (x +y\right )\right )}{y}=0} \]
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 {x}{y}\right ] \\ \\ \end{align*}