Link to actual problem [2352] \[ \boxed {\frac {1}{{y^{\prime }}^{2}}+y^{\prime } x -2 y=0} \]
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 [\underline {\hspace {1.25 ex}}\xi &= \frac {3 x}{2}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \left [R &= \frac {y}{x^{\frac {2}{3}}}, S \left (R \right ) &= \frac {2 \ln \left (x \right )}{3}\right ] \\ \end{align*}