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Math Help - Differential equation - population of a city

  1. #1
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    Differential equation - population of a city

    A model for the population of a city is given by:

    \frac{dp}{dt} = -4*10^{-8}p^2 + 0,56p -16*10^5

     p(0) = 6*10^6


    And then I should find an expression for the population, p(t) (after t years). But how do I begin? The right side can also be written like: -4*10^{-8}(p-10^7)(p-4*10^6)
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  2. #2
    A Plied Mathematician
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    The equation is separable.
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  3. #3
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    Quote Originally Posted by Ackbeet View Post
    The equation is separable.
    like:

    -\frac{1}{4*10^{-8}}\int\frac{1}{(p-10^7)(p-4*10^6)} dp = \int 1 dt ?
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  4. #4
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    Looks good so far! I'd use partial fractions on the LHS.
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