Link to actual problem [1438] \[ \boxed {x^{2} \left (1+2 x \right ) y^{\prime \prime }-x \left (9+8 x \right ) y^{\prime }-12 y x=0} \] 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], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
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 {\left (2 x +1\right )^{4} y}{x^{10}}\right ] \\ \end{align*}