Consider the initial value problem dy dt

= (y − 1)

2



t − y +

3 2



with y(0) = 0.

a. Find a value of y 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 at t = 1, t = 2 and t = 3. Where necessary, you may round off your results to 4 decimal places. Present your results in a table with columns for tn, yn, f (tn, yn)

and yn+1.

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

d. What will be the long-term behaviour of the solution as calculated by Euler’s method with step size h = 1?

e. Is the long-term behaviour of the true solution the same as the behaviour calculated by Euler’s method with step size h = 1? Explain your answer.