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How to Solve the Following D.E.?

  1. Sep 10, 2006 #1
    Hi guys,

    I'm stuck trying to separate the following equation, not really sure how so separate it:

    [​IMG]

    Thanks for any inputs!
     
    Last edited: Sep 10, 2006
  2. jcsd
  3. Sep 10, 2006 #2

    arildno

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    You can't separate it as it stands, so play a bit around by trying to change the independent or dependent variable.
     
  4. Sep 10, 2006 #3
    Could you explain how that would work? You're right, it's supposed to be x(y) and when y=1, x=3. But I'm not sure how to put that info to use. TIA.
     
    Last edited: Sep 10, 2006
  5. Sep 10, 2006 #4

    arildno

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    Well, lets for fun's sake make our new dependent variable:
    [tex]u(x)=9-5xy^{2}(x)\to{y(x)=\sqrt{\frac{9-u}{5x}}[/tex]
    Now, find an expression for dy/dx and y^3 in terms of x and u.

    Substitute all of this into your diff.eq, if you are lucky, you've gotten a separable diff.eq in u and x.
    Probably, it won't work with this choice; you can have hours of fun trying out different changes of variable. :smile:
     
  6. Sep 10, 2006 #5
    Thanks, with your help I was able to figure out the answer. Much appreciated!
     
  7. Sep 11, 2006 #6

    HallsofIvy

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    Try an integrating factor of the form yn.
     
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