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Homework Help: Laplace transform initial value problem

  1. Dec 2, 2009 #1
    1. The problem statement, all variables and given/known data

    Use the Laplace transform to solve the following initial value problem:
    x' = 7 x + 5 y, y'= -2 x + e5t, x(0)=0, y(0)=0

    Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s)

    2. Relevant equations

    3. The attempt at a solution
    I'm confused on how to deal with the the x and y in each equation. We didn't do an example like this in class so I'm a little lost. We did it with one equation, but not two. Any help would be greatly appreciated!
    Last edited: Dec 3, 2009
  2. jcsd
  3. Dec 3, 2009 #2


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    Science Advisor

    Then take the Laplace transform of both x and y! It's exactly the same. You will get two equations for the two Laplace transforms. Solve for each transform, then take the inverse transform to find x and y. It might be a good idea to let the variable be the usual "s" in one transform and, say, "t" in the other.
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