Link to actual problem [11918] \[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x +\frac {3 y}{4}=0} \] 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
[[_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*} \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= x^{2}, \underline {\hspace {1.25 ex}}\eta &= \frac {3 x y}{2}\right ] \\ \left [R &= \frac {y}{x^{\frac {3}{2}}}, S \left (R \right ) &= -\frac {1}{x}\right ] \\ \end{align*}