Finding Non-trivial solutions to ODE in Mathematica

[sci-phy]

For an ODE of order 2 like:

X'' + λ*X = 0, how do I find the non-trivial solution in Mathematica 8? It's giving me only the trivial solution.

In: ComplexExpand [DSolve[{u''[x] + \[Lambda]^2 u[x] == 0, u[0] == 0, u[a] == 0}, u[x], x]]

and the out: u[x]--> 0 which is the trivial soln

Thanks

 

[fzero]

You've set $u(a)=0$ without placing any conditions on $a$. Try using rewriting $a$ in terms of an appropriate multiple of $\lambda$.