Link to actual problem [2360] \[ \boxed {y-y^{\prime } x -{\mathrm e}^{y^{\prime }}=0} \]
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 &= -\frac {-y+x \ln \left (x \right )}{x}, S \left (R \right ) &= \ln \left (x \right )\right ] \\ \end{align*}