Link to actual problem [8908] \[ \boxed {f \left (x -\frac {3 {y^{\prime }}^{2}}{2}\right )+{y^{\prime }}^{3}-y=0} \]
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}{D\left (f \right )\left (x -\frac {3 {\operatorname {RootOf}\left (f \left (x -\frac {3 \textit {\_Z}^{2}}{2}\right )+\textit {\_Z}^{3}-y \right )}^{2}}{2}\right )}, \underline {\hspace {1.25 ex}}\eta &= 1\right ] \\ \operatorname {FAIL} \\ \end{align*}