Consider the following initial value problem dq dw

= (q − 2) (w − q) with q(−2) = 1

a. Find a value of q for which the solution to the differential equation is a constant. (This solution need not satisfy the initial value.)

b. Use Euler’s method with step size h = 1 to estimate the solution to this initial value problem at w = −1, w = 0 and w = 1. Where necessary, you may round off your results to 4 decimal places. Present your results in a table with columns for wn, qn, f (wn, qn) and qn+1.

c. Use a computer to calculate and plot the solution for this equation.

d. What is the long-term behaviour of the solution to this initial value problem as calculated by Euler’s method with step size h = 1?

e. Is the behaviour of the true solution the same as the behaviour calculated by Euler’s method with step size h = 1?

Explain your answer.