Chapter 3.3, Problem 19E

The slope field for the system
$\begin{array}{l}\frac{dx}{dt}=-2x+\frac{1}{2}y\hfill \\ \frac{dy}{dt}=-y\hfill \end{array}$
is shown to the right.
(a) Determine the type of the equilibrium point at the origin.
(b) Calculate all straight-line solutions.
(c) Plot the $x(t)$ - and $y(t)$ -graphs, $(t\ge 0)$
for the initial conditions $A=(2,1)$
$B=(1,-2),C=(-2,2),$ and $D=$
$(-2,0)$