It's taken me ages, and I really am struggling to understand this, so I am not sure if this is correct but here goes...
\bigtriangledown^2 G = \delta(\underline{x} - \underline{x}_0) \frac{\partial G(x,0)}{\partial y} = 0 for y \geq 0 \ - \infty < x < \infty
Let r = |\underline{x} -...
Use the method of images to find a Green's function for the problem in the attached image.
Demonstrate the functions satisfies the homogenous boundary condition.