Link to actual problem [6970] \[ \boxed {x \left (1+x \right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y=0} \] With the expansion point for the power series method at \(x = -1\).
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 {y}{x^{2}+4 x +5}\right ] \\ \end{align*}