Help Solving an Equation with a Boundary Condition

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FranciscoSili
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Hello everybody. I'm about to take a final exam and I've just encountered with this exercise. I know it's simple, but i tried solving it by Separation of variables, but i couldn't reach the result Mathematica gave me. This is the equation:
∂u/∂x = ∂u/∂t
Plus i have a condition: u(x,1)=Exp[2*(x-1)^2]

I'd be very grateful if someone can answer this. And sorry i didn't type the equations in a correct way. I just don't know how.

Thank you in advance :D
 
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