dx/dt = x − xy      dy/dt = xy − y

where: x represents prey density and y represents predator density. Create a vector field for this system. The predator should be represented on the y-axis and the prey should be represented on the x-axis. Consider values 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3. Hint: divide the two differential equations.

) Write a procedure that generates a plot of a ‘rose’. If the number of petals is even, have your procedure colour in the petals aquamarine, if the number of petals is odd, colour in the petals pink.

Test your procedure by generating two flowers, one with an even number of petals and one with an odd number of petals.

Consider the function f(x, y) = (x − 3)(y − 2) − 2.

Create a contour plot of f(x, y). Include 20 contour lines.