Link to actual problem [5477] \[ \boxed {x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x y \left (x^{2}+1\right )=0} \] With the expansion point for the power series method at \(x = 0\).
type detected by program
{"second order series method. Regular singular point. Repeated root"}
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 &= -\frac {x}{2}, \underline {\hspace {1.25 ex}}\eta &= x^{2} y\right ] \\ \\ \end{align*}