Exercise 9

Consider the initial value problem $$\begin{gathered} \frac{dy}{dt} = -\frac ty, \ y(0) = 8 \end{gathered}$$

1. Find the solution of the initial value problem and sketch its graph.

2. For what values of $t$ is the solution defined?

3. What is the value of $y$ at the last time that the solution is defined?

4. By looking at the differential equation, explain why we should not expect to find solutions with the value of $y$ you noted in (c).