Link to actual problem [7871] \[ \boxed {x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y=0} \]
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}{-1+x}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {{\mathrm e}^{x} y}{\left (-1+x \right ) \operatorname {expIntegral}_{1}\left (-x \right )+{\mathrm e}^{x}}\right ] \\ \end{align*}