A classical model used to study interacting populations is the

x' = a x - b x y, x(0) = 80 y' = -c y + d x y, y(0) = 30 where a = 0.25, b = 0.01, c = 1.0 and d = 0.01.

- Use Euler's method with h = 0.4 ( n=200) and h = 0.1 ( n= 800) to approximate the solution. Graphically display the results in the phase plane (x,y).
- Use
*dsolve*with the numeric option to constuct the solution for t in [0,80] and graphically display the results. - Write a discussion comparing the results.
- By eliminating the t varlable, derive and graph an implicit solution f(x,y) in the phase plane (x,y). What special properties, if any, does the graph of this solution reveal? What further conclusions can you make about the numerical approximations.