Link to actual problem [14398] \[ \boxed {y-t \left (2-y^{\prime }\right )-2 {y^{\prime }}^{2}=1} \]
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 {t}{2}-2, \underline {\hspace {1.25 ex}}\eta &= -\frac {t}{2}+y -5\right ] \\ \left [R &= -\frac {-y+3+t}{\left (t -4\right )^{2}}, S \left (R \right ) &= 2 \ln \left (t -4\right )\right ] \\ \end{align*}