question 11:

(d) (2 points) Consider again an initial population of PTO) = 15. Give your long-term predictions for this population, with explicit reference to each of your answer in (b) and your phase line diagram in (c). Explain and justify your answer succinctly and clearly. (c) (2 points) Identify all equilibria of the differential equation and draw the phase line diagram corresponding to this system. Label each equilibrium as stable or unstable on your diagram. Show your work. (b) (1 point) Suppose initially P(U} = 15. What is the particular Solution in this case? PG) = 11. (5+1+2+2=10 points, over two pages) The autonomous differential equation dP = 2P2 TOP + 500. dt models the dynamics of a town population, with immigration and emigration. (a) (5 points) Rewrite this differential equation to show that it is separable, then solve it. Your answer must express P as a function of t