Link to actual problem [4282] \[ \boxed {2 x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2}=x} \]
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 &= \frac {y}{x}, S \left (R \right ) &= \ln \left (x \right )\right ] \\ \end{align*}