Use a CAS to explore graphically each of the differential equations. Perform the following steps to help with your explorations.

a. Plot a slope field for the differential equation in the given xy-window.

b. Find the general solution of the differential equation using your CAS DE solver.

c. Graph the solutions for the values of the arbitrary constant C = -2, -1, 0, 1, 2 superimposed on your slope field plot.

d. Find and graph the solution that satisfies the specified initial condition over the interval [0, b].

e. Find the Euler numerical approximation to the solution of the initial value problem with 4 subintervals of the x-interval and plot the Euler approximation superimposed on the graph produced in part (d).

f. Repeat part (e) for 8, 16, and 32 subintervals. Plot these three Euler approximations superimposed on the graph from part (e).

g. Find the error (y(exact) - y(Euler)) at the specified point x = b for each of your four Euler approximations. Discuss the improvement in the percentage error.

y′ = y(2 - y), y(0) = 1/2; 0 ≤ x ≤ 4, 0 ≤ y ≤ 3; b = 3