Chapter 10.5, Problem 7E

One or more initial conditions are given for each differential equation in the following exercises. Use the qualitative theory of autonomous differential equations to sketch the graphs of the corresponding solutions. Include a $yz$-graph if one is not already provided. Always indicate the constant solutions on the $ty$-graph whether they are mentioned or not.

$y^{\prime }=3-\frac{1}{2}y$, $y(0)=4$, $y(0)=8$.[The graph of $z=g(y)$ is drawn in fig. $12$.]