1. The problem statement, all variables and given/known data Given the partial differential equation: ∂2u/∂x2 = ∂2u/∂t2 , where x[0;L] Use separation of variables to find the solution that satisfies the boundary conditions: ∂u/∂x (x=0) = ∂u/∂x (x=L) = 0 2. Relevant equations The separation of variables method. 3. The attempt at a solution I think I have found a way to do the problem. There are just minor things that I want to clear up. So let's jump into it: Assuming a solution of the form u(x,y) = X(x)T(t) gives the equations: X'' = -k2X T'' = -k2T with the solutions: X = Acos(kx)+Bsin(kx) T=Ccos(kx)+Dsin(kx) and with the boundary conditions we must have that; X'(0)=X'(L)=0 which gives: -Aksin(0)+Bkcos(0) = 0 => Bk=0 which must imply that B=0 From that we get: -Aksin(kL)=0 => kL = (n+½)∏ => kn = (n+½)∏/L So the general solution is: ƩAcos(knx)T where sum is from -∞ to ∞. Is this correct? Now my teacher has uploaded a paper with solutions and in his expression there is no A. Is this just because the A has been absorbed into the constants of T, or shouldn't it be there at all? Also, I find it kind of weird to be choosing the constant -k2. I do so because I've been told that, but why do you that? Also my teacher notes, that choosing k2 would instead yield a trivial solution? Can anyone explain to me why this is and why you don't just choose a trivial constant c?