Link to actual problem [4285] \[ \boxed {x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }=-1} \]
type detected by program
{"clairaut"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], _Clairaut]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \left [R &= \frac {y}{x^{\frac {1}{3}}}, S \left (R \right ) &= \frac {\ln \left (x \right )}{3}\right ] \\ \end{align*}