We have analysed the logistic equation, but in its simplest form it can be solve

Question

We have analysed the logistic equation, but in its simplest form it can be solved exactly as a separable DE. Consider the example problem; dP/dt = 1/2(4-P),P(0) = 2 What are the intrinsic growth rate and the carrying capacity of this system? Find the equilibrium points and test their stability. Indicate what will happen as t rightarrow infinity. Solve the equation exactly and check the solution by substitution (as in Q1). Verify the limiting behaviour as determined in (b). Hint: Partial fractions gives 1/x(a - x) = 1/ax + 1/a(a - x)

Explanation / Answer

a. 0.5*2*2=2 b.p=0,4 p=4 stable as t-> infinity, p-> infinity c. ques1 is required

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