(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

X''+[tex]\lambda[/tex]*X=0 0<x<2pi

X(0)=X(2pi) and X'(0)=X'(2pi)

2. Relevant equations

3. The attempt at a solution

My only problem is the case when [tex]\lambda[/tex]=0

in such case the general solution is X(x)= C1+C2*x

Now, after applying the BCs, this is what I get:

C1=C2*2pi

and

C2=C2

now, what should C2 be ? zero or any value ?

if C2 is zero, we have the trivial solution only. However, if C2 is any number, we have a nontrivial solution.

how can I solve this question?

Thanks.

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# ODE/PDE- eighenvalues question

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