Undergrad Help Solving an Equation with a Boundary Condition

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The discussion revolves around solving the equation ∂u/∂x = ∂u/∂t with the boundary condition u(x,1)=Exp[2*(x-1)^2]. The user attempted to apply the method of Separation of Variables but could not match the solution provided by Mathematica. They express concern about the simplicity of the problem and their formatting of the equations. The user seeks assistance from the forum community to clarify their approach and find the correct solution. The thread highlights the challenges of solving differential equations with specific boundary conditions.
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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