where initial conditions are w(x,0) = w(x,b) = w(0,y) = w(a,y) = 0

poisson's equation is d2w/dx2+d2w/dy2 = f(x,y)

if we assume a 1D eigenfunction expansion:

w(x,y) = Sum(a_n(y) * sin(n*pi*x/a)

Obtain the ode and BCs for each a_n(y).

I know you can split this into a homogeneous solution and a particular solution, but how can you get the particular solution?

Or does someone else have a better method of solving this?

And also, we have to solve this by hand. No Matlab.\

Thanks!