Link to actual problem [4339] \[ \boxed {\ln \left (y^{\prime }\right )+a \left (x y^{\prime }-y\right )=0} \]
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 &= y+\frac {\ln \left (x \right )}{a}, S \left (R \right ) &= -\frac {\ln \left (x \right )}{a}\right ] \\ \end{align*}