Help Solving an Equation with a Boundary Condition

In summary, the boundary condition for an equation is determined by the specific problem being solved and is typically given as a set of values or constraints at the boundaries of the problem domain. Its purpose is to specify the behavior of the solution at the boundaries and provide additional information to help solve the equation. It is incorporated into the equation by setting up additional equations or conditions that must be satisfied at the boundaries. A boundary condition can change the solution of an equation by restricting possible solutions or altering the nature of the solution. Different types of equations have different types of boundary conditions.
  • #1
FranciscoSili
8
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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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1. How do I determine the boundary condition for an equation?

The boundary condition for an equation is determined by the specific problem being solved. It is typically given as a set of values or constraints at the boundaries of the problem domain.

2. What is the purpose of a boundary condition in an equation?

The boundary condition is used to specify the behavior of the solution at the boundaries of the problem domain. It provides additional information to help solve the equation and obtain a unique solution.

3. How do I incorporate the boundary condition into the equation?

The boundary condition is incorporated into the equation by using it to set up additional equations or conditions that must be satisfied at the boundaries. These conditions are then solved along with the original equation to obtain a solution that satisfies both the equation and the boundary condition.

4. Can a boundary condition change the solution of an equation?

Yes, a boundary condition can affect the solution of an equation. It can restrict the possible solutions or even change the nature of the solution, such as causing a discontinuity or singularity.

5. Are there different types of boundary conditions for different types of equations?

Yes, there are different types of boundary conditions depending on the type of equation being solved. For example, there are different boundary conditions for ordinary differential equations, partial differential equations, and integral equations.

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