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Solving Diff EQ using a Laplace Transform

  1. May 6, 2007 #1

    G01

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    1. The problem statement, all variables and given/known data
    Solve the initial value problem:

    [tex] \frac{dy}{dt} + 2y = u_2(t)e^{-t}[/tex]

    y(0) = 3

    Where [tex]u_2(t)[/tex] is a Heaviside Function with the discontinuity at t=2.

    2. Relevant equations
    The Laplace transform of a Heaviside function multiplied by another function:

    [tex] L( u_a(t)f((t-a) ) = e^{-as}L(f(t-a))[/tex] Where L denotes the laplace tranform of a function.


    3. The attempt at a solution

    I know that in order to solve this equations using a laplace transform, I need to convert the RHS to the form of function in part 2. above. Once I do that I can take the Laplace Transform of both sides and then solve for L(y) and then y. I've been working at this for a while now, and I'm stuck on converting the RHS into a function whose transform I know. If I get this, then I can definitely do the rest of the problem. Any hints of converting this function into a workable form will be greatly appreciated.
     
  2. jcsd
  3. May 6, 2007 #2

    G01

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    Figured it out! Thanks anyway!
     
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