Link to actual problem [4719] \[ \boxed {x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y=0} \] 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}{x^{4}}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x \left (\operatorname {expIntegral}_{1}\left (x \right ) x^{3} {\mathrm e}^{x}-x^{2}+x -2\right )}\right ] \\ \end{align*}