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Tricky differential equation

  1. Oct 12, 2011 #1
    1. The problem statement, all variables and given/known data

    Hint: Eliminate the first derivative term

    2. Relevant equations

    3. The attempt at a solution

    I have tried lots of substitutions, but none of them seems to work out. I don't really understand what the hint is getting at. For example, I've tried y'=ux, but then I don't know what to do with the y. I've tried y=ux, but that doesn't seem to help matters at all. And I've tried numerous other silly things that haven't worked out. I'm really out of ideas and stuck. Any little hints would be greatly appreciated.
  2. jcsd
  3. Oct 12, 2011 #2


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    Science Advisor
    Homework Helper

    You notice that xy'' + y' looks very much like the derivative of a product.

    So I suggest you try playing around with u = xy' or x(y'2); and if that doesn't work maybe u = xy
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