In Problems 1-3,find the constant solution(s) x(t) = kfor each second-order equation, and
determine the behiJvior as follows:
(a) Rewrite the equation as a system of two first-order equations.
(b) Find the equilibrium solution(s) of the equivalent first-order system.
(c) Deduce the behavior of the trajectories about the fixed point as I --+ oo-for example, flying away from the fixed point, orbiting it, approaching it.
(d) Describe the physical behavior of solutions to the DE. Tell what it means for a mass-spring system.
1. x" + x' + x = O
2. x" - x' + x = 0
3. x" + x = l