# Question:laplace equation with pdsolve and boundary conditions

## Question:laplace equation with pdsolve and boundary conditions

Maple 13
Hi there

I'm working with maple 13

I got stuck with the problem below, maybe one of the experts out there could give me a hand

>
restart;
with(PDETools); with(ArrayTools);
pde := k^2*(diff(phi(x, z), x, x))+diff(phi(x, z), z, z) = 0;
sol1 := pdsolve(pde, HINT = X(x)*Z(z));
>
so far so good. I would like to find a way to determine _c1 (which I know equals to -1). When I replace _c1 for -1, I get the ODE's that I'm looking for
>
#_c1=-1
eq1 := diff(X(x), x, x) = -X(x);
dsolve(eq1);
eq2 := diff(Z(z), z, z) = k^2*Z(z);
dsolve(eq2);

I am not quite sure how to insert my boundary conditions into my problem, they are
>
bc[1] := -(diff(phi(x, z = -d), z)) = 0;
bc[2] := diff(phi(x = 0, z), x) = diff(phi(x = 2*pi, z), x);
>
I would like suggestions on how to solve this either using pdsolve or manually. Any tips are greatly welcomed.

Thank you for yout time in advance

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