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Homework Help: Bernoulli's o.d.e

  1. Feb 18, 2010 #1
    1. The problem statement, all variables and given/known data
    [tex] \frac{dy}{dx}= - \frac{c}{n} y^{n} [/tex]


    2. Relevant equations


    [tex] y' + p(x)y=q(x) y^n [/tex]

    3. The attempt at a solution
    im strictly speaking able to do it , i just wanted to kno whether im on the right track using bernoulli's equation, not that i can see any other methods!
    ;-)
    cheers
     
  2. jcsd
  3. Feb 18, 2010 #2

    rock.freak667

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    If c and n are constants then you can just divide by yn and you'd have a separable ODE
     
  4. Feb 18, 2010 #3
    thanks , i try that ( c and n are constants). seems less involving if not actually suggesting i was on the wrong track
     
  5. Feb 18, 2010 #4

    LCKurtz

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    Gold Member

    I don't think you will find it to be separable. Bernoulli's method is the way to go. Dividing by yn puts it in the form

    y(-n)y' +p(x)y(1-n)= q(x)

    and the change variable v = y(1-n) transforms it into a linear first order equation which can be done with an integrating factor.

    [edit] Correction -- your specific equation is indeed separable, it is the general Bernoulli equation that isn't.
     
    Last edited: Feb 18, 2010
  6. Feb 18, 2010 #5
    i did find it to be separable and got an expression for a problem im working on that agrees with the solution provided, so im confident about that . thanks though.

    here's the source of the d.e. for the curious :
    https://www.physicsforums.com/showthread.php?p=2587065#post2587065
     
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