Link to actual problem [14049] \[ \boxed {x {y^{\prime \prime }}^{2}+2 y=2 x} \]
type detected by program
{"unknown"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries]]
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 &= -\frac {2 x}{3}+y\right ] \\ \left [R &= -\frac {x -y}{x^{3}}, S \left (R \right ) &= 3 \ln \left (x \right )\right ] \\ \end{align*}