I'm working on the same problem. Was there also a dielectric problem in this set? I made a post about it.
Also, we are given V(x,0) and V(y,0) are these the same as X(x) and Y(y). And where did you plug into get Z(z)? I'll see what I can get, just reply or private message me if you did the...
Homework Statement
A point charge q is a distance d from a dielectric half-space (z < 0). We will
solve for the potential outside of the dielectric, in the region z > 0.
(a) Away from the point charge, what equation does V satisfy? Find the bound-
ary conditions at the dielectric...