Link to actual problem [7560] \[ \boxed {\left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y=0} \]
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 {{\mathrm e}^{x} y}{x \left (x -4\right ) \left (2+x \right )^{2}}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {{\mathrm e}^{x} y}{{\mathrm e}^{-2} x \left (x -4\right ) \left (2+x \right )^{2} \operatorname {expIntegral}_{1}\left (-x -2\right )+\left (x^{3}-x^{2}-10 x -6\right ) {\mathrm e}^{x}}\right ] \\ \end{align*}