Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2004 / Paper 1 / 6 / i / Solution

An ordinary point of the normalized second-order equation is a point where both coefficient functions $p(x)$ and $q(x)$ are analytic in a neighborhood. Ordinary continuity is enough for a local existence theorem, but analyticity is the condition used for a convergent local power series solution.