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Fast help please: solving differential equations

  1. May 20, 2009 #1
    1. The problem statement, all variables and given/known data
    I have the equation -(ck^2)U(k,t)=d^2/dt U(k,t). And I need to find the general solution.


    2. Relevant equations



    3. The attempt at a solution
    I can rearrange this into the form d^2 U/dt^2 + (ck^2)U(k,t)=0 but I am not sure of the form of the solution to this equation.

    could someone please give me pointer in the right direction
     
  2. jcsd
  3. May 20, 2009 #2
    Is it just U(k,t) = Acos(ckt)+Bcos(ckt)?
     
  4. May 20, 2009 #3
    Yeah, it's just the differential equation for SHM so that is the solution.
     
  5. May 20, 2009 #4

    dx

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    Gold Member

    No it's not. You will get a constant when you do the integration with respect to t, and this constant can depend on k. So the general solution is what you wrote + f(k), where f(k) is an arbitrary function of k.

    EDIT: You should have (√c)k instead of ck in the sin and cos.
     
  6. May 20, 2009 #5

    dx

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    Oops! I'm extremely sorry, my previous post is wrong. The constants A and B are the constants of integration, and they should be arbitrary functions of k.
     
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