Find the first two terms in an asymptotic expansion as $x \to 0^+$ of two independent solutions of $y''(x)=\sqrt{x}y(x)$.
$x=0$ if we keep $0$ positive does not appear to be a singularity. So I assume we are looking for the asymptotic expansion around an ordinary point rather then a singular point. My initial approach would be to plug in a power series centered around zero and find out the coefficients. I want to check with you guys if that is the right approach. If not can you give me a nudge in the right direction? Thanks