Analysis Question--differentiabillity, continuity
Homework Statement
Suppose f:\mathbb{R}\to\mathbb{R} is a C^\infty function which satisfies the equation f''(x)=-x^2f(x) along with f(0)=1, f'(0)=0. Prove that there is an a>0 such that f(a)=0. Do not use any results from differential...