Chapter 3.6, Problem 17P

For each of the systems in Problem $13$ through $20$:

a) Find all of the critical points.

b) Use a computer, to draw a direction field and phase portrait for the system.

c) From the plots in part (b), describe how the trajectories behave in the vicinity of each critical point.

$\frac{dx}{dt}=y\left(2-x-y\right),\frac{dy}{dt}=-x-y-2xy$