Find the solution of Laplace's equation u + Uyy = 0 within the rectangle 0 < x < 2, 0 < y < 4, which satisfies the boundary conditions u(0, y) = 0, u(2, y) = 0, u(x,0) = 0, u(x,4) = 3. Write down the complete solution u(x, y) and give the first two non-zero terms of the series.

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