Use the method of separation of variables to find the natural frequencies (i.e the in the equation where T=T(t) ) for the waves which satisfy the equation

where k>0 and c>0 are constants with

I can get to the point of separating the equation to get 2 DE'S to solve, but I'm a bit stuck as to where to go from there. I've got that,

and

Using the boundary conditions I get that X(0)=0 and X(l)=0, should I use these to solve the first equation involving X?

Any help much appreciated!