Link to actual problem [2350] \[ \boxed {3 {y^{\prime }}^{4} x -{y^{\prime }}^{3} y=1} \]
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 {4 x}{3}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \left [R &= \frac {y}{x^{\frac {3}{4}}}, S \left (R \right ) &= \frac {3 \ln \left (x \right )}{4}\right ] \\ \end{align*}