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Two Partial Differential Equations

  1. Feb 20, 2012 #1
    1. The problem statement, all variables and given/known data
    This is the first problem of the two.

    2. Relevant equations



    3. The attempt at a solution

    Using separation of variables, I end up with

    T'(t)= -λKT(t) and X''(x)+(β/K)X'(x)/X(x)= -λ. At first I chose the negative lambda because I saw that U(0,t) and U(L,t) needed to oscillate and I was hoping to get a sin function. Now the characteristic equation for X is something like r^2 + (β/K)r +λ=0 and I am not sure if I am on the right track in solving for the function X(x).
     

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    Last edited: Feb 20, 2012
  2. jcsd
  3. Feb 20, 2012 #2
    You're on the right path, but it helps to use 2 instead of λ.
     
  4. Feb 20, 2012 #3
    thanks. I guess what I should have said is that I am stuck at this point.
     
  5. Feb 20, 2012 #4
    Solve the characteristic equation for r. The solution has the form C1Exp(rx)+C2Exp(-rx).
    This might become D1sin(r'x)+D2cos(r'x) depending on the sizes of β, k, and λ.
    Edit:If r was imaginary, r' is a new constant that is real.
     
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