Link to actual problem [7254] \[ \boxed {\left (y-2 y^{\prime } x \right )^{2}-{y^{\prime }}^{3}=0} \]
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 &= \frac {x}{3}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \left [R &= \frac {y}{x^{3}}, S \left (R \right ) &= 3 \ln \left (x \right )\right ] \\ \end{align*}