Chapter 3.6, Problem 15P

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.

$\frac{dx}{dt}=x-x^2-xy,\frac{dy}{dt}=\frac{1}{2}y-\frac{1}{4}{y}^2-\frac{3}{4}xy$