(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have the solution to the differential equation : Phi = A*sin(x) + B*cos(x) and need to apply the boundary conditions Phi(-a/2) = Phi(a/2) = 0.

2. Relevant equations

3. The attempt at a solution

I am confused. If I plug these in, then I get

A*sin(-ka/2) = - B*cos(-ka/2) and since cos is even, cos(-x) = -cos(x) and sin is odd, so using these we get

Asin(ka/2) = B cos(ka/2).

Similarly, with ka/2 we get that Asin(ka/2) = - B cos(ka/2). But Asin(ka/2) = B cos(ka/2) as well, so doesn't this imply that B=-B so that B must be 0?

That's what I thought...

but the answer to my original problem gives both a sine and cosine solution to Phi. I'm very confused about how this is possible if B = 0, I must be making a mistake somewhere. Am I supposed to infer instead that ka/2 = n*Pi/4?? I'm quite confused.

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# Homework Help: Boundary value problem

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