Consider the initial value problem dy dt

= (3 − y)(y + 1) with y(0) = 1.

a. Use Euler’s method with step size h = 1 to estimate the solution at t = 1, t = 2 and t = 3.

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

c. 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.
Hint: use a qualitative analysis to find the steady states, and determine which are sinks and which are sources. Use this to predict the longterm behaviour of the true solution.

d. Calculate and plot the true solution.