x^2y'' + xy' + (x^2-p^2)y=0
so when p=0 the non-trivial solution is

y_0= \sum_0^{\infty} \frac{(-1)^n}{(n!)^2}(\frac{x}{2})^{2n}

How do you find r?

y=x^r \sum_0^\infty C_nX^n ?