Chapter 3.2, Problem 6E

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.
6. $\frac{dx}{dt}=5x+4y$
$\frac{dy}{dt}=9x$