Chapter 3.2, Problem 22E

In Exercises 21-24, we return to Exercises 1-4 in Section 2.3 . (For convenience, the equations are reproduced below.) For each second-order equation,
(a) convert the equation to a first-order, linear system;
(b) compute the eigenvalues and eigenvectors of the system;
(c) for each eigenvalue, pick an associated eigenvector $V,$ and determine the solution $Y(t)$ to the system; and
(d) compare the results of your calculations in part (c) with the results that you obtained when you used the guess-and-test method of Section 2.3
22. $\frac{d^{2}y}{d{t}^2}+5\frac{dy}{dt}+6y=0$