Chapter 3.5, Problem 1E

In Exercises 1-4, each of the linear systems has one eigenvalue and one line of eigenvectors. For each system,
(a) find the eigenvalue;
(b) find an eigenvector;
(c) sketch the direction field;
(d) sketch the phase portrait, including the solution curve with initial condition $Y_0=(1,0);$ and
(e) sketch the $x(t)$ - and $y(t)$ -graphs of the solution with initial condition $Y_0=(1,0)$

1. $\frac{d\text{Y}}{dt}=\left(\begin{array}{rr}\hfill -3& \hfill 0\\ \hfill 1& \hfill -3\end{array}\right)\text{Y}$