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Non-Linear Separable D.E.

  1. Sep 28, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]\frac{dy}{dx}+2xy^{2}=0[/tex]

    I am stuck on this.

    I realize that this is a non-linear exact equation, but I just cannot wrap my mind around any type of method to attack this one.

    TIA for any help
     
  2. jcsd
  3. Sep 28, 2009 #2

    LCKurtz

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    You noticed it is separable, so just separate the variables.
     
  4. Sep 28, 2009 #3
    Okay, never-mind...

    Problem:

    [tex]\frac{dy}{dx}+2xy^{2}=0[/tex]

    Solution:

    [tex]\frac{dy}{dx}=-\left(2xy^{2}\right)[/tex]

    [tex]\left(\frac{1}{y^{2}}\right)\frac{dy}{dx}=-2x[/tex]

    [tex]\int\frac{1}{y^{2}} dy=-2\int x dx[/tex]

    [tex]y=\frac{1}{x^{2}+C_{1}}[/tex]
     
  5. Sep 28, 2009 #4
    Yeah, my CalIII is killing me...

    Thanks for the response. I hope the next time I have a question, it will be a good one :redface:
     
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