Link to actual problem [4338] \[ \boxed {\ln \left (y^{\prime }\right )+4 x y^{\prime }-2 y=0} \]
type detected by program
{"dAlembert"}
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 [R &= y+\frac {\ln \left (x \right )}{2}, S \left (R \right ) &= -\frac {\ln \left (x \right )}{2}\right ] \\ \end{align*}