Link to actual problem [7484] \[ \boxed {y^{\prime \prime } x^{2}-x \left (x +6\right ) y^{\prime }+10 y=0} \] 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^{5} \left (x +4\right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\left (x^{3} {\mathrm e}^{x} \left (x +4\right ) \operatorname {expIntegral}_{1}\left (x \right )-x^{3}-3 x^{2}+2 x -2\right ) x^{2}}\right ] \\ \end{align*}