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Hard Laplace Transform pde

  1. Sep 28, 2009 #1
    1. The problem statement, all variables and given/known data
    Help, I don't know how to do the following question:

    Using Laplace to solve
    x' -y =1
    2x' +x +y' = (t2-2t+1)e-(t-1)

    2. Relevant equations
    x(1)=0
    y(3)=0


    3. The attempt at a solution
    The problem i'm having is the initial conditions aren't at zero, and I'm not sure how to approach the question

    so far I have:
    X(s) -x(0) -Y(s) = 1/s
    3X(s) -2x(0) +Y(s)-y(0)= F{(t2-2t+1)e-(t-1)}
     
  2. jcsd
  3. Sep 28, 2009 #2

    LCKurtz

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    Gold Member

    This isn't a pde. It is a system of ordinary DE's. And you have mistakes in your transforms.

    L(x') is not X(s) - x(0) it is sX(s) - x(0), and ditto for y'. And, of course, you need to transform (t2-2t+1)e-(t-1).

    Just call x(0) = a and y(0) = b and leave them in there. Once you get the equations right and solve for X(s) and Y(s), you can take the inverse transforms. Your answers will have a and b in them. Finally, plug in your given initial conditions and choose a and b to make them work.
     
  4. Sep 29, 2009 #3
    Thanks alot LCKurtz, I didn't see that mistake. and the solution makes more sense now. I was getting weird answer from other questions too and could work out why.
     
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