Link to actual problem [4031] \[ \boxed {{y^{\prime }}^{2}+2 x y^{\prime }-y=0} \]
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 {x}{2}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \left [R &= \frac {y}{x^{2}}, S \left (R \right ) &= 2 \ln \left (x \right )\right ] \\ \end{align*}