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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.