1. The problem statement, all variables and given/known data Solve: ∂u/∂t = k ∂2u/∂x2 - ζu with the initial condition u(x,0) = f(x) where k and ζ are constants. x is on an infinite domain. 2. Relevant equations Define Fourier transforms: f(x) = ∫[-∞,∞]F(w)e-iwxdw F(w) = 1/2∏ ∫[-∞,∞]f(x)eiwxdx From tables of Fourier Transforms: ∂2f/∂x2 = (-iw)2F(w) 3. The attempt at a solution I have little experience with transforms so please don't berate me if this is completely wrong. Began by taking transform of entire eqn: F(∂u/∂t) = k F(∂2u/∂x2) - ζF(u) I will call F(u) = U* ∂U*/∂t = w2k U* - ζU* ∂U*/∂t = (w2k - ζ) U* So the general solution is: U* = C(w) e(w2k-ζ)t Where C(w) = 1/2∏ ∫[-∞,∞]f(x)eiwxdx Is this even remotely correct? It seems too easy, but then again, I suppose that is the point of transforms, to put something into a simpler form.