Link to actual problem [15108] \[ \boxed {y-x \left (1+y^{\prime }\right )-{y^{\prime }}^{2}=0} \]
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 [\underline {\hspace {1.25 ex}}\xi &= 1, \underline {\hspace {1.25 ex}}\eta &= 1-\frac {x}{2}\right ] \\ \left [R &= y+\frac {x^{2}}{4}-x, S \left (R \right ) &= x\right ] \\ \end{align*}