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Math Help - Continuous Model

  1. #1
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    Continuous Model

    This is actually a problem for my calculus class but it's mostly diff. eq.

    Given I'(t)=aI(N-I) with the initial condition I(0)=1

    solve this equation and show that the solution can be written as:

    I(t)=N/(1+Be^(-aNt))

    any help would be greatly appreciated.
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  2. #2
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    \frac{dI}{dt} = aI(N-I)
    \frac{dI}{aI(N-I)} = dt
    Try to find
    \frac{1}{aI(N-I)} = \frac{z1}{aI} + \frac{z2}{N-I}.
    Find z1 and z2.
    Integration give left side will be two functions ln, right t+C.
    Last edited by zzzoak; April 1st 2010 at 03:57 PM.
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  3. #3
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    so it looks like I'm to use fractional decomposition. Which Still has me stumped.
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