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Integrator factor

  1. Sep 13, 2006 #1
    Hi guys, i need your help. I am not sure what is the integrator factor in this diferential equation to start solving it.

    xy' + 2y = sin(x)

    Thanks a lot
     
  2. jcsd
  3. Sep 13, 2006 #2
    You need to first write it as
    y' + p(x)y = q(x)

    Then evaluate
    [tex] \mu = exp(\int p(x) dx) [/tex]

    Is that what you mean by integrating factor?
     
  4. Sep 13, 2006 #3

    HallsofIvy

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    Staff Emeritus
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    Or, if you would prefer to derive it yourself, an integrating factor is a function p(x) such that multiplying the equation by it, the left side becomes an "exact derivative":
    [tex]\frac{d(p(x)xy)}{dx}= p(x)x\frac{dy}{dx}+ 2p(x)y[/tex]
    Since
    [tex]\frac{d(p(x)xy)}{dx}= p(x)x\frac{dy}{dx}+ p(x)y+ p'(x)xy[/itex]
    that means we must have xp'+ p= 2p or xp'= p, a simple separable differential equation for p. Solving it you get exactly what LeBrad said.
     
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