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Wave equation with initial and boundary conditions.

  1. May 14, 2010 #1
    Hallo Every one,

    1. The problem statement, all variables and given/known data

    y(x,t)=sin(x)cos(ct)+(1/c)cos(x)sin(ct)

    Boundary Condition:

    y(0,t)=y(2pi,t)=(1/c)sin(ct) fot t>0

    Initial Condition :

    y(x,0)=sin(x),( partial y / Partial t ) (x,0) = cos(x) for 0<x<2pi


    show that y(x,t)=sin(x)cos(ct)+(1/c)cos(x)sin(ct) satisfies the one dimensional wave equation together with boundary and initial conditions.



    Please any one can clearify the question for me so i can solve it.
     
    Last edited: May 14, 2010
  2. jcsd
  3. May 14, 2010 #2
    Just i want to know how i can prove that the given function satisfies the Boundary condition and initial condition.
     
  4. May 14, 2010 #3

    Cyosis

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    Homework Helper

    The boundary and initial conditions have been given. Now you just have to plug the appropriate values for x and t belonging to said conditions into your solution.
     
  5. May 14, 2010 #4
    iam not trying to slove the boundary value problem

    i want to prove that the given function satisfy the boundary and initial condition.
     
  6. May 14, 2010 #5

    Cyosis

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    Homework Helper

    Yep and post #3 gave you the method as to how to do just that.

    Hint: what is the x value that belongs to the given boundary condition?
     
  7. May 14, 2010 #6
    thanks Cyosis

    Just i concentrate and i solve it
     
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