Link to actual problem [8935] \[ \boxed {y^{\prime }-\frac {F \left (-\left (-y+x \right ) \left (y+x \right )\right ) x}{y}=0} \]
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 &= \frac {1}{x}, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{y}\right ] \\ \left [R &= -x^{2}+y^{2}, S \left (R \right ) &= \frac {x^{2}}{2}\right ] \\ \end{align*}