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 Recognitions: Gold Member So this gives me $\mathbb{F} _c ^{-1} [U_c(p,x)]=u(x,y)=\frac{2}{\pi} \int _0 ^{\infty} U_c (p,x) \cos (py)dp$. Is this ok? $U_c(p,x)=Ae^{px}+Be^{-px}$. So that $u(x,y)=\frac{2}{\pi} \int _0 ^{\infty } (Ae^{px}+Be^{-px} ) \cos (py)dp$. This doesn't look a correct answer to me though, let alone how to simplify it and calculate A and B from the boundary conditions.