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Homework Help: Differential Equation population question.

  1. Feb 3, 2010 #1
    Hi could someone please explain how this can be done please

    The population P satisfies the differential equation
    dt = X(P) − Y(P) , where X(P) is the birth rate and Y(P) is the death rate. Find the general solution P(t) to this differential equation for the case that X(P) = k1(sqrt)P and Y(P) = k(sqrt)P , where k1 and k2 are positive constants. In the case k2 > k1, determine the time t0 at
    which the population has died out if the population at time t = 0 was P0.

  2. jcsd
  3. Feb 3, 2010 #2


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    Homework Helper

    Well, it looks like your ODE is dP/dt=k1*sqrt(P)-k2*sqrt(P)=(k1-k2)*sqrt(P). You usually start to solve something like that by separating the variables. Can you get started?
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