Link to actual problem [3904] \[ \boxed {x \left (x^{3}-3 y x^{3}+4 y^{2}\right ) y^{\prime }-6 y^{3}=0} \]
type detected by program
{"unknown"}
type detected by Maple
[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
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 {x^{4}}{y^{2}}, \underline {\hspace {1.25 ex}}\eta &= 0\right ] \\ \left [R &= y, S \left (R \right ) &= -\frac {y^{2}}{3 x^{3}}\right ] \\ \end{align*}