Series Solutions · Challenge problem

The equation $(1 - x)(2 - x)\,y' = (x - 3)\,y$ has singular points $x = 1$ and $x = 2$, so the ordinary-point theorem only guarantees that the power-series solution about $0$ with $y(0) = 1$ converges for $|x| < 1$. Find the actual radius of convergence of that series.