Consider the second-order equation where p and q are positive. (...

Consider the second-order equation

where p and q are positive.

(a) Convert this equation into a first-order, linear system.

(b) Compute the characteristic polynomial of the system.

(c) Find the eigenvalues.

(d) Under what conditions on p and q are the eigenvalues two distinct real numbers?

(e) Verify that the eigenvalues are negative if they are real numbers.