Link to actual problem [9582] \[ \boxed {\left (x^{2}+x -2\right ) y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }-\left (6 x^{2}+7 x \right ) y=0} \]
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}^{-2 x} y}{-1+x}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {{\mathrm e}^{3 x} y}{-195 \,{\mathrm e}^{-5} {\mathrm e}^{5 x} \left (-1+x \right ) \operatorname {expIntegral}_{1}\left (5 x -5\right )+x +44}\right ] \\ \end{align*}