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Separable Differential Equation

  1. Sep 6, 2012 #1
    1. The problem statement, all variables and given/known data

    Solve the given differential equation by separation of variables.



    2. Relevant equations

    dP/dt = P - P2

    3. The attempt at a solution

    This is no problem to "solve" except that Webassign (:cry:) wants to know the whole thing in terms of P.

    You end up with

    dP/(P-P2) = dt

    which is not a difficult integral, but you end up with a left side: (after "e-ing" both sides) of P-P^2. How can I give this in terms of P, or am I thinking wrong? (probably the latter)

    -Dave K
     
  2. jcsd
  3. Sep 6, 2012 #2

    SammyS

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    I'm assuming that P2 is really P2 .

    What is P2 equal to after you integrate?

    Don't you have an equation which is quadratic in P ?
     
  4. Sep 7, 2012 #3
    Yes, you're correct, it's P^2 (Sorry about that). I suppose yes, it's a quadratic. Let me see what happens.
     
  5. Sep 7, 2012 #4

    ehild

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    So your equation is
    [tex]\int{\frac{dp}{p-p^2}dp}=\int{dt}[/tex]

    Factor out p in the denominator: it becomes a product. You can resolve the LHS integrand to partial fractions.

    ehild
     
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