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A Hard differential equation

  1. Sep 28, 2007 #1
    A Hard differential equation!!!!

    Solve:

    dy/dx = (x^2) + y
     
  2. jcsd
  3. Sep 28, 2007 #2
    The rules of this forum requires you to show some working, so that we know where to begin helping.

    Can you solve the homogeneneous equation: dy/dy - y = 0 ?
    Can you find a particular integral?
     
  4. Sep 28, 2007 #3

    HallsofIvy

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    That is a first order linear differential equation with constant coefficients- actually, it's about the easiest you could come up with. genneth suggested solving the "homogeneous equation" first. That would work.

    But for linear first order equations, there is a standard formula for the "integrating factor". You could also use that.
     
  5. Sep 28, 2007 #4

    mjsd

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    relevant equation:
    if [tex]\frac{dy(x)}{dx}+P(x)\,y(x) = Q(x)[/tex]
    then
    [tex]y(x) = e^{-\int P(\eta)\,d\eta} \int Q(x)\;e^{\int P(\xi)\,d\xi}\,dx[/tex]

    if you understand this you probably understand how to do your problem :smile:
     
  6. Sep 28, 2007 #5
    thx guys


    so........

    first i should write it in the form

    dy/dx + (-1)y = (x^2)

    is that right?
     
    Last edited: Sep 28, 2007
  7. Sep 28, 2007 #6

    mjsd

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    the next step into better understanding this is to prove the formula above...
     
  8. Oct 18, 2007 #7
    Proof hint

    The way I always proved this was to make the differential equation exact first. Then the rest is algebra; ahem, calculus.
     
  9. Oct 20, 2007 #8
    dy/dx-y=x^2 is a good start

    To make your integrating factor, you do Exp(integral(-1dx)) (i hope that makes sense). Work it from there and see where you get.
     
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