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.