Question: To model a conflict between two guerrilla armies, we assume that the rate that each one is put out of action is proportional to the product of the strengths of the two armies.
(a) Write the differential equations which describe a conflict between two guerrilla armies of strengths x and y, respectively.
(b) Find a differential equation involving dy/dx and solve to find equations of phase trajectories.
(c) Describe which side wins in terms of the constant of integration. What happens if the constant is zero?
(d) Use your solution to part (c) to divide the phase plane into regions according to which side wins.