Link to actual problem [7816] \[ \boxed {x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y=0} \]
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*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x^{3}-12 x^{2}+60 x -120}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {{\mathrm e}^{x} y}{x^{3}+12 x^{2}+60 x +120}\right ] \\ \end{align*}