Problem 5
Consider the autonomous differential equation given by:
$$ \frac{dy}{dx} = (y - 2)(y + 1)(y - 4) $$
where $\frac{dy}{dx}$ is a function of $y$.
a) State the equilibrium solutions.
b) Construct a phase line and decide for each equilibrium solution whether it is locally
stable or not.
c) In the xy-plane, sketch the equilibrium solutions and the solution curves that pass
through the indicated points (0, -2), (0, -1), (0, 1), (0, 2), (0, 3), (0, 4) and (0, 5).
Problem 6
A local health clinic monitors two conditions: high cholesterol and diabetes. For the
patients examined in the clinic, the probability of having high cholesterol is 0.25, the
probability of having diabetes is 0.40, and the probability of having both high cholesterol
and diabetes is 0.10.
a) Find the probability of having either condition or both.
b) Find the probability of not having either condition.
