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Intial value problem

  1. Nov 30, 2008 #1
    1. The problem statement, all variables and given/known data

    let f(t) = t if 0<t<1
    1 if 1<t

    y" +4y = f(t)
    y(0)=0 and y'(0)=0

    2. Relevant equations



    3. The attempt at a solution

    I took g(t)= t(u)t+(1-t)u(t-1)
    so then I got
    (1/s^2)+e^-2s((-1/s^2)+(2/s))
    which goes to
    (1/(1-e^-2s))((1-e^-2s-2se^-2s)/s^2)

    now I think
    Y=L{y(t)}(s)
    L{y'}=sY
    L{y"}=s^2Y

    so (s^2)Y+4Y f(t)
    Y(s^2 + 4)=f(t)

    so
    Y(s^2 + 4)=(1/(1-e^-2s))((1-e^-2s-2se^-2s)/s^2)

    Now what do I do from here? If I solve for Y I get

    Y=(1/(1-e^-2s))((1-e^-2s-2se^-2s)/s^2)(1/(s^2 +4)

    but now what?
     
  2. jcsd
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