Link to actual problem [6883] \[ \boxed {\left (y^{\prime }+1\right )^{2} \left (-y^{\prime } x +y\right )=1} \]
type detected by program
{"clairaut"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], _dAlembert]
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 x}{2}, \underline {\hspace {1.25 ex}}\eta &= -\frac {x}{2}+y\right ] \\ \left [R &= \frac {x +y}{x^{\frac {2}{3}}}, S \left (R \right ) &= \frac {2 \ln \left (x \right )}{3}\right ] \\ \end{align*}