Link to actual problem [8959] \[ \boxed {y^{\prime }-\frac {i x^{2} \left (i-2 \sqrt {-x^{3}+6 y}\right )}{2}=0} \]
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}{x^{2}}, \underline {\hspace {1.25 ex}}\eta &= {\frac {1}{2}}\right ] \\ \left [R &= y-\frac {x^{3}}{6}, S \left (R \right ) &= \frac {x^{3}}{3}\right ] \\ \end{align*}