1 (c) (12 pts) Consider the logistic equation IP 3 Use phase portrait analysis to classify the equilibrium solutions as asymptotically stable, 10 unstable or semi-stable. (ii) Find the general so...
For the equation (dp/dt)=(P+2)(P^2-6P+5) find the equilibrium points and make a phase portrait of the differential equation. Classify each equilibrium point as asymptotically stable, unstable or semi-stable. Sketch typical solution curves determined by the graphs of equilibrium solutions.
dP 7. For the equation = (P+2)(P2 - 6P+5)find the equilibrium points and make a phase dt portrait of the differential equation. Classify each equilibrium point as asymptotically stable, unstable or semi-stable. Sketch typical solution curves determined by the graphs of equilibrium solutions. (6pts)
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical points). b) (3 points) Use the sign of y f(z) to determine where solutions are increasing / decreasing. Sketch several solution curves in each region determined by the critical points in c) (3 points) the ty-plane. d) (3 points) Classify each equilibrium point as asymptotically stable, unstable, or semi-stable and draw the corresponding phase line. 4 Consider the autonomous differential equation y f(v)...