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Homework Help: Piecewise continuous - step function

  1. Dec 6, 2009 #1
    1. The problem statement, all variables and given/known data
    Consider the following initial value problem:

    y''+4y = 9t, 0<=t<2
    ............0, t>=2

    Find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)

    2. Relevant equations

    3. The attempt at a solution
    I am just having trouble with the step function:

    Say g(t)= 9t, 0<=t<2
    ...............0, t>=2

    g(t)= (1-u(t-2))9t ???
    = 9t-u(t-2)9t

    So, Laplace{g(t)} = (9-9e-2s)/(s2)

    SO, s2Y(s) + 4Y(s) = (9-9e-2s)/(s2)

    And, Y(s) = (9-9e-2s)/((s2)(s2+4))

    There is something wrong with this. If anyone could help me out that would be much appreciated!! Thanks!
    Last edited: Dec 6, 2009
  2. jcsd
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