Help Solving an Equation with a Boundary Condition

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SUMMARY

The discussion centers on solving the partial differential equation ∂u/∂x = ∂u/∂t with the boundary condition u(x,1) = Exp[2*(x-1)^2]. The user attempted to apply the Separation of Variables method but was unable to match the results produced by Mathematica. The conversation highlights the importance of correctly applying mathematical techniques and understanding boundary conditions in solving PDEs.

PREREQUISITES
  • Understanding of partial differential equations (PDEs)
  • Familiarity with the Separation of Variables technique
  • Basic knowledge of boundary conditions in mathematical analysis
  • Experience with Mathematica for computational verification
NEXT STEPS
  • Study the method of Separation of Variables in detail
  • Learn how to apply boundary conditions effectively in PDEs
  • Explore Mathematica's capabilities for solving differential equations
  • Review examples of similar PDEs with boundary conditions for better understanding
USEFUL FOR

Students preparing for exams in mathematics or physics, educators teaching differential equations, and anyone interested in advanced mathematical problem-solving techniques.

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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