1. The problem statement, all variables and given/known data Let V be the real functions y=f(x) satisfying d^2(y)/(dx^2) + 9y=0. a. Prove that V is a 2-dimensional real vector space. b. In V define (y,z) = integral (from 0 to pi) yz dx. Find an orthonormal basis in V. 3. The attempt at a solution part A: I integrated and got that f(x)= (-3/2)y^3 + Cy, C is a real number. It seems like I need to use dot product here. I don't know how, though. part B: Completely lost.