Link to actual problem [6994] \[ \boxed {x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (1+x \right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
type detected by program
{"second order series method. Regular singular point. Difference is integer"}
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}{\operatorname {BesselI}\left (1, x\right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {{\mathrm e}^{-x} y}{\operatorname {BesselK}\left (1, x\right )}\right ] \\ \end{align*}