Chapter 2.3, Problem 6E

In the damped harmonic oscillator, we assume that the coefficients m, b, and k are positive. However, the rationale underlying the guess-and-test method made no such assumption, and the same analytic technique can be used if some or all of the coefficients of the equation are negative. In Exercises 5 and 6, make the same graphs and perform the same calculations as were specified in Exercises 1—4. What is different in this case?

6. $\frac{d^{2}y}{d{t}^2}+\frac{dy}{dt}-2y=0$