To account for seasonal variation in the logistic differential equation we could allow

Chapter 9, Problem 38

(choose chapter or problem)

To account for seasonal variation in the logistic differential equation we could allow and to be functions of : (a) Verify that the substitution transforms this equation into the linear equation (b) Write an expression for the solution of the linear equation in part (a) and use it to show that if the carrying capacity is constant, then Deduce that if , then . [This will be true if with , which describes a positive intrinsic growth rate with a periodic seasonal variation.] (c) If is constant but varies, show that and use lHospitals Rule to deduce that if has a limit as , then has the same limit.