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Homework Help: Differential equations help.

  1. Feb 19, 2008 #1
    Hey, everyone. I've been doing my Calculus II homework, and I've been trying these two problems for the past few hours, but I can't even seem to get started on them. A friend of mine recommended I try here because you guys are awesome.

    1. The problem statement, all variables and given/known data
    The Gompertz equation
    dP/dt = P(a - b ln(P))
    where a and b are positive constants, is another model of population growth.
    a) Find the solution of this differential equation that satisfies the initial condition: P(0) = p(sub(0))
    b) What happens to P(t) as t -> infinity?
    c) Determine the concavity of the graph of P

    2. The attempt at a solution

    dP/dt = P(a - bQ)
    where Q = ln(x)​

    1. The problem statement, all variables and given/known data

    the differential equation
    dP/dt = P(10^-1 - (10^-5)P)
    models the population of a certain community. Assume P(0) = 2000 and time t is measured in months.
    a) Find P(t) and show that lim t -> infinity exists
    b) Find the limit

    2. The attempt at a solution

    I do not even know where to start on this. Any help at all would be nice.
  2. jcsd
  3. Feb 19, 2008 #2
    Write it as
    [tex]\frac{d\,P}{P\,(a-b\,\ln P)}=d\,t[/tex]
    and set [itex]\ln P=u[/itex]
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