Series Solutions · Hard problem

The equation $(x^2 - 6x + 10)\,y'' + xy' + y = 0$ has complex singular points at $3 \pm i$. For what value of $k < 3$, if the power series is expanded about $x_0 = k$ instead of $x_0 = 0$, does the ordinary-point theorem guarantee a radius of convergence of exactly $\sqrt5$?