Populations of aphids and ladybugs are modeled by the equations dA/dt = 2A 0.01AL dL/dt = 0.5L

Question:

Populations of aphids and ladybugs are modeled by the equations dA/dt = 2A €“ 0.01AL dL/dt = €“ 0.5L + 0.0001AL
(a) Find the equilibrium solutions and explain their significance.
(b) Find an expression for dL/dA.
(c) The direction field for the differential equation in part (b) is shown. Use it to sketch a phase portrait. What do the phase trajectories have in common?
(d) Suppose that at time t = 0 there are 1000 aphids and 200 ladybugs. Draw the corresponding phase trajectory and use it to describe how both populations change.
(e) Use part (d) to make rough sketches of the aphid and ladybug populations as functions of . How are the graphs related to each other?