What is wrong here? (A differential equation)

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Jamin2112
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What is wrong here? (A differential equation)

Homework Statement



My homework has a Sturm-Louiville eigenvalue problem

Lu = u'' - u = 0, x ε (0,1)​

with u(0)=u(∏)=0. The only solution is u(x) = 0, x ε [0,1]. Right? But then other parts of this particular problem become trivial.

Homework Equations



Nothing really

The Attempt at a Solution



Plugged it into Wolfram Alpha to get u(x)=0, solved it using the characteristic equation to get u(x)=0, and also did the eigenfunction expansion to get the same answer.
 
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nevermind! I just saw fredholm's alternative in the lecture notes. I get it now.