Find the solution of the equation using a given f(x)

[Susanne217]

Homework Statement

I have the heat equation $$\frac{\partial u}{\partial t} = k \frac{\partial^2 u}{\partial x^2}$$

where u(x,0) = f(x) and $$f(x) = \frac{sin(x)}{x}$$

use the expression of the Fourier Integral to calculate u(x,t).

Homework Equations

The Attempt at a Solution

Do I simply plug this into the general product solution for u(x,t)??

 

[rock.freak667]

When you get your solution for u(x,t), put t=0 and then equate that to sin(x)/x.