Link to actual problem [8843] \[ \boxed {9 y^{4} \left (x^{2}-1\right ) {y^{\prime }}^{2}-6 x y^{5} y^{\prime }=4 x^{2}} \]
type detected by program
{"unknown"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
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 {3 y^{3}}{4 x}, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{y^{2}}\right ] \\ \left [R &= y^{6}+4 x^{2}, S \left (R \right ) &= \frac {y^{3}}{3}\right ] \\ \end{align*}