Query 08 Differential Equations

Question:  3.5.6.  Solve the equation dPdt = r ( 1 - P / P_c) P + M with r = 1, P_c = 1 and M = -1/4.

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3.5.10.  Solve dP/dt = k ( N - P) * P with P(0) = 100 000 assuming that P is the number of people, out of a population of N = 500 000, with a disease.  Assume that k is not constant, as in the standard logistic model, but that k = 2 e^(-t) - 1.  Plot your solution curve and estimate the maximum value of P, and also that value of t when P = 50 000.  Interpret all your results in terms of the given situation.

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