- #1

fk378

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## Homework Statement

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.

## 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.