Chapter 3.2, Problem 1E

In Exercises $1-10$

(a) compute the eigenvalues;

(b) for each eigenvalue, compute the associated eigenvectors;

(c) using HPGSystemsolver, sketch the direction field for the system, and plot the straight-line solutions;

(d) for each eigenvalue, specify a corresponding straight-line solution and plot its $x(t)$ and $y(t)$ -graphs; and

(e) if the system has two distinct eigenvalues, compute the general solution.

1. $\frac{dY}{dt}=\left(\begin{array}{rr}\hfill 3& \hfill 2\\ \hfill 0& \hfill -2\end{array}\right)Y$