The concentrations of two chemicals A and B as functions of time are denoted by x and y respectively. Each alone decays at a rate proportional to its concentration. Put together, they also interact to form a third substance, at a rate proportional to the product of their concentrations. All this is expressed in the equations:

dx/dt = −2x−xy,

dy/dt = −3y−xy.

Note that (x, y)=(0,0) is the only equilibrium state (both concentrations must be positive or zero).

(a) Find an equation for y(x):
dy/dx =

(b) Solve your equation to obtain a relationship between x and y. Letting x(0)=5 and y(0)=10, give the relationship as an equation involving x and y:

(Your answer will be an equation involving x and y.)

Note that one implication of your relationship should be that if x and y are positive and very small (so that x is very much smaller than ln(x)), y2/x3 is roughly constant.

(c) Suppose that x=y. From your equation, what are x and y in this case?
x = y=