This problem focuses on using MATHCAD, an ordinary differential equation (ODE) solver, and also a nonlinear equation (NLE) solver.

(a) There are initially 500 rabbits (x) and 200 foxes (y) on Farmer Oats property near Ria, Jofostan.

Use MATHCAD to plot the concentration of foxes and rabbits as a function of time for a period of up to 500 days. The predatorprey relationships are given by the following set of cou- pled ordinary differential equations:

dx/dt = k1 x k2xy dt

dy/dt = k3 x y k4 y dt

Constant for growth of rabbits k1 = 0.02 day1

Constant for death of rabbits k2 = 0.00004/(day no. of foxes)

Constant for growth of foxes after eating rabbits k3 = 0.0004/(day no. of rabbits)

Constant for death of foxes k4 = 0.04 day1

What do your results look like for the case of k3 = 0.00004/(day no. of rabbits) and tfinal = 800 days? Also, plot the number of foxes versus the number of rabbits. Explain why the curves look the way they do.

(b) Use MATHCAD to solve the following set of nonlinear algebraic equations (x^3)y4(y^2) +3x = 1

6(y^2 ) 9xy = 5

with inital guesses of x = 2, y = 2 .