11. (5+1+2+2=10 points, over two pages) The autonomous differential equation dP dt 2P2 70P + 500. 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. (b) (1 point) Suppose initially P(0) = 15. What is the particular solution in this case? P(t) = = 11, continued. Recall that dP 2P2 70P + 500. dt (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. (d) (2 points) Consider again an initial population of P(0) = 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