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April 10th, 2015, 05:13 PM   #1
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From: Sylmar

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Population Model-logistic nonlinear first-order ordinary differential equation

I have to find the explicit solution to this harvesting problem in a population model where dN/dt=rN(1-N/K)-H(N) such that H=qEN, subject to initial condition N(0)=N_0. Here N=N(t) and r,K,q, and E are positive constants. I also have to deduce the two limiting behaviors as t approaches infinity. So far I have broken down the equation to (1/N)dN/dt+(r/k)N=(r-qE). Any hints on how to do the problem would be very much appreciated. I'm having trouble understanding what they mean by finding the explicit solution and deducing two limiting behaviors.
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differential, differential equation, equation, first order, firstorder, mathematical modeling, modellogistic, nonlinear, ordinary, population, population model



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