Link to actual problem [8943] \[ \boxed {y^{\prime }-\frac {-3 y x^{2}+F \left (y x^{3}\right )}{x^{3}}=0} \]
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 {3 y}{x}\right ] \\ \\ \end{align*}