Link to actual problem [1205] \[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +6 y=0} \] With the expansion point for the power series method at \(x = 0\).
type detected by program
{"second order series method. Ordinary point", "second order series method. Taylor series method"}
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}}{2}-\frac {1}{2}, \underline {\hspace {1.25 ex}}\eta &= x y\right ] \\ \\ \end{align*}