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Integrating Factor Question

  1. Nov 20, 2009 #1
    So there's this equation:
    [tex]x^2 y^2 dx + (x^3y-1)dy[/tex]
    It has to be solved with the integrating factor method, so I get this:
    [tex]\mu(y) = e^{\int \frac{dy}{y}} = e^{\ln{|y|}} = |y|[/tex]

    My question is, what do I do with the absolute value bars?
    If I just drop them and multiply the entire equation with y, then I can solve the equation and get:
    [tex]2x^3 y^3 - 3 y^2 = C[/tex]
    Which is the correct answer.
    But I'm not sure that dropping it will always be correct, so what should be done here?
     
  2. jcsd
  3. Nov 20, 2009 #2
    what is [itex]\ln(-1)[/itex]?
     
  4. Nov 21, 2009 #3
    It's undefined, and I know that.
    This is the reason you put the bars in the first place, but my question was about the integrating factor itself, should it be y or |y|.
     
  5. Nov 21, 2009 #4

    HallsofIvy

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    Use either y or -y. Since you are multiplying the entire equation by that, it doesn't affect the result.
     
  6. Nov 21, 2009 #5
    ok I understand!
     
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