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Homework Help: Ordinary Differential Equations

  1. Mar 7, 2010 #1
    1. The problem statement, all variables and given/known data

    Give the general solution to the IVP

    L[y]=y'+(sint)y=[tex]\delta[/tex](t-[tex]\tau[/tex])
    y(0)=0

    For all t>0 by placing a jump condition on y(t) and solving the differential equation for t<[tex]\tau[/tex] and t>[tex]\tau[/tex]

    2. Relevant equations



    3. The attempt at a solution

    I'm plenty sure I can get the general solution to the problem, but I do not at all know how to get the "jump condition" as it wasn't explained in lectures or in the textbook. Your help is very much appreciated.
     
    Last edited: Mar 7, 2010
  2. jcsd
  3. Mar 7, 2010 #2

    vela

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    Integrate the differential equation from [itex]\tau-\varepsilon[/itex] to [itex]\tau+\varepsilon[/itex] and take the limit as [itex]\varepsilon\rightarrow 0[/itex]. That will give you a result that tells you how big the discontinuity in y(t) is at [itex]t=\tau[/itex].
     
  4. Mar 7, 2010 #3
    So what would we get when we integrate [tex]\delta[/tex](t-[tex]\tau[/tex])? would it be 1?
     
  5. Mar 7, 2010 #4

    vela

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    Yes, because the interval of integration includes the point [itex]t=\tau[/itex].
     
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