- #1

Roni1985

- 201

- 0

## Homework Statement

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

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

## Homework Equations

## 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.