Link to actual problem [4035] \[ \boxed {{y^{\prime }}^{2}+2 \left (1-x \right ) y^{\prime }+2 y=2 x} \]
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 {x^{2}}{2}, S \left (R \right ) &= x\right ] \\ \end{align*}