Link to actual problem [2532] \[ \boxed {z y^{\prime \prime }-2 y^{\prime }+9 z^{5} y=0} \] With the expansion point for the power series method at \(z = 0\).
type detected by program
{"second order series method. Regular singular point. Difference is integer"}
type detected by Maple
[[_Emden, _Fowler], [_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 [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= {\mathrm e}^{i \sqrt {z^{4}}\, z}\right ] \\ \left [R &= z, S \left (R \right ) &= {\mathrm e}^{-i \sqrt {z^{4}}\, z} y\right ] \\ \end{align*}