Link to actual problem [11289] \[ \boxed {x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+y \left (x +1\right )=x^{2}-x -1} \]
type detected by program
{"kovacic"}
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*} \\ \\ \end{align*}
\begin{align*} \\ \\ \end{align*}