Link to actual problem [6976] \[ \boxed {x y^{\prime \prime }+\left (3+2 x \right ) y^{\prime }+4 y=0} \] 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 [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{x^{2}}\right ] \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {{\mathrm e}^{-2 x} \left (2 x +1\right )}{x^{2}}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {x^{2} {\mathrm e}^{2 x} y}{2 x +1}\right ] \\ \end{align*}