Heat equation, Fourier cosine transform

fluidistic

So this gives me [itex]\mathbb{F} _c ^{-1} [U_c(p,x)]=u(x,y)=\frac{2}{\pi} \int _0 ^{\infty} U_c (p,x) \cos (py)dp[/itex]. Is this ok?
[itex]U_c(p,x)=Ae^{px}+Be^{-px}[/itex]. So that [itex]u(x,y)=\frac{2}{\pi} \int _0 ^{\infty } (Ae^{px}+Be^{-px} ) \cos (py)dp[/itex]. 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.

fluidistic Recognitions: Gold Member	So this gives me [itex]\mathbb{F} _c ^{-1} [U_c(p,x)]=u(x,y)=\frac{2}{\pi} \int _0 ^{\infty} U_c (p,x) \cos (py)dp[/itex]. Is this ok? [itex]U_c(p,x)=Ae^{px}+Be^{-px}[/itex]. So that [itex]u(x,y)=\frac{2}{\pi} \int _0 ^{\infty } (Ae^{px}+Be^{-px} ) \cos (py)dp[/itex]. 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.