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Differental Equation homework (w/ calc 2 intergrals)

  1. Jan 28, 2013 #1
    1. The problem statement, all variables and given/known data
    Carrying capacity N of a population

    Assume: small population, dp/dt is proportional to P

    if 0<P<N then p(t) increases
    if P>N then P(t) decreases
    equilibrium means dp/dt = 0


    2. Relevant equations
    dP/dT = KP(N-P)

    Solve for P(t)


    3. The attempt at a solution
    ∫dP/P(N-P) = ∫kdt ?

    My teacher said we'd be using ln(...) and 1/[P(N-P)] = A/P + B/(N-P)


    Please help! Thanks. :)
     
  2. jcsd
  3. Jan 28, 2013 #2

    LCKurtz

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    You are on the right track. Perhaps you need to review partial fractions to work the integral$$
    \int \frac{1}{P(N-P)}\, dP$$Your teacher gave you a pretty good hint there.
     
  4. Jan 28, 2013 #3
    I can solve it from here I don't know why I was so confused. :) thanks
     
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