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Homework Help: How to solve this First Order Differential Equation?

  1. Sep 27, 2011 #1
    How to solve this differential equation?

    dy/dx = - (3yx^(2) + y^(2)) / (2x^(3) + 3xy)

    I've tried finding an integrating factor in order to make it exact, but I don't know what to do with this.

    The answer is given as x^(3)y^(2) + xy^(3) = c

    I'm so confused.

    I separated it and found My and Nx. I've also tried finding an integrating factor, but it isn't a function of 'xy'.
    Last edited: Sep 27, 2011
  2. jcsd
  3. Sep 27, 2011 #2


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    Presumably you have written it in the form

    (3x2y+y2)dx + (2x3+3xy)dy = 0

    You are correct that it is not exact. But it may have an integrating factor that is a function of x or y only which will make it exact. Look at


    I think you will find one of those two tests works.
  4. Sep 27, 2011 #3
    Eh, I just found out what I did wrong. Simple mistake, but took hours to find it because I kept doing it.... was dividing by N instead of M....

    but Thank you for your assistance!
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