Link to actual problem [14810] \[ \boxed {x y^{\prime \prime }+2 y^{\prime } x +y=0} \] 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}{\left (\operatorname {BesselI}\left (0, x\right )-\operatorname {BesselI}\left (1, x\right )\right ) x}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {{\mathrm e}^{x} y}{x \left (\operatorname {BesselK}\left (0, -x \right )-\operatorname {BesselK}\left (1, -x \right )\right )}\right ] \\ \end{align*}