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## Homework Statement

Solve the heat equation

[itex]\frac{∂}{∂t}[/itex]u[itex](x,t)[/itex]=[itex]\frac{1}{α^2}[/itex][itex]\frac{∂^2}{∂t^2]}[/itex]u(x,t)

on the real line ℝ with the initial conditions:

u(x,0)= 1 if |x| [itex]\leq[/itex]1, 0 for any other value of x

## Homework Equations

I don't even know where to start for this question, but I believe that I will have to use a fourier transform, and perhaps separation of variables, to find a solution to this problem

## The Attempt at a Solution

I don't even know where to start.

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