please solve this question 1. Consider the following modified Logistic model to describe a population p -p(t) with stronger competition as time t increases: dys Here the net birth rate is 1 and the c...
1. Consider the following modified Logistic model to describe a population p -p(t) with stronger competition as time t increases: dys Here the net birth rate is 1 and the competition term is (1 - e ')p with constant a > 0 (a) Make a substitution of the form u p for some integer m and so reduce (1) to the linear first Cl order o.d.e du dt (b) Find the general solution of (1) (c) If we define thecying capacity to be lim p(t), then what is the yng capacity of (1)? (d) Solve (1) subject to the conditions a 4 and p(0) Please turn over]
1. Consider the following modified Logistic model to describe a population p -p(t) with stronger competition as time t increases: dys Here the net birth rate is 1 and the competition term is (1 - e ')p with constant a > 0 (a) Make a substitution of the form u p for some integer m and so reduce (1) to the linear first Cl order o.d.e du dt (b) Find the general solution of (1) (c) If we define thecying capacity to be lim p(t), then what is the yng capacity of (1)? (d) Solve (1) subject to the conditions a 4 and p(0) Please turn over]