Link to actual problem [8945] \[ \boxed {y^{\prime }-\frac {-2 x -y+F \left (\left (y+x \right ) x \right )}{x}=0} \]
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 &= 1, \underline {\hspace {1.25 ex}}\eta &= -\frac {y}{x}-2\right ] \\ \\ \end{align*}