Consider the differential equation dP dt = P(P 1)(2 P). (a) Find all the equilibrium
Chapter 0, Problem 58(choose chapter or problem)
Consider the differential equation dP dt = P(P 1)(2 P). (a) Find all the equilibrium solutions. (b) Show that the following two functions are solutions: P1(t)=1 et 3 + e2t and P2(t) = 1+ et 3 + e2t . [Hint: Use a computer algebra system to simplify the difference between the right and left-hand sides.] (c) Find P1(0), P2(0), limt P1(t), and limt P2(t). Explain how you could have predicted the limits as t from the values at t = 0 without knowing the solutions explicitly.
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