Find the Fourier transform \hat{u}(w,t) = \frac{1}{\sqrt{2 \pi}} \int^{\infty}_{- \infty}u(x,t)e^{(-ixw)}dx of the general solution u(x,t) of the PDE u_{t}= u_{xx} - u Should I start by solving the PDE, or is there another way to do it?