Series Solutions · Challenge problem

The equation $(x^2 + 1)(x^2 - 6x + 10)\,y'' + y = 0$ is to be solved by power series about a real centre $x_0$, and the series must be guaranteed (by the ordinary-point theorem) to converge at every point of the interval $0 \le x \le 3$. The set of centres $x_0$ that work is an interval. Find its length. Express your answer as a common fraction.