Link to actual problem [5489] \[ \boxed {2 x y^{\prime \prime }-y^{\prime }+y x^{2}=0} \] With the expansion point for the power series method at \(x = 0\).
type detected by program
{"second order series method. Regular singular point. Difference not 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}^{\frac {i x^{\frac {3}{2}} \sqrt {2}}{3}}\right ] \\ \left [R &= x, S \left (R \right ) &= {\mathrm e}^{-\frac {i x^{\frac {3}{2}} \sqrt {2}}{3}} y\right ] \\ \end{align*}