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PDE involving Fourier Sine Series

  1. Dec 2, 2012 #1
    1. The problem statement, all variables and given/known data
    Solve:
    PDE: 9Uxx=Utt
    BC: U(0, t) = U(∏, t) = 0
    IC: U(x, 0) = sin4x + 7sin5x
    Ut = x 0 < x < ∏/2
    = ∏ - x ∏/2 < x < ∏

    2. Relevant equations

    Fourier Sine Series and Cosine Series Equations

    3. The attempt at a solution

    (see attached photo)

    I am getting very lost at the tail end of this problem (the bottom right hand portion of the attached photo). I can't seem to really figure out how to apply the Fourier Sine Series equations with the given PDE. Any help would be truly appreciated!
     

    Attached Files:

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  2. jcsd
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