1. Consider the second order DE 3:" + ax'[3:2 + (3.)2 1) + m = U, a gt; I]. [a] Rewrite the equation as a rst order system. [b] Show that the

1. Consider the second order DE3:” + ax’[3:2 + (3.")2 — 1) + m = U, a > I]. [a] Rewrite the equation as a first order system. [b] Show that the curve :32 + y? = 1 is invariant with respect to the flow of the system.Explain why this curve is a periodic orbit. [c] Find a the periodic solution of the system associated with the periodic orbit, that is, find at] = (61(t),.f2[t)) such that at) satisfies the system, at + T) = {(t) forsome T :> U and {it}? +§2{t)2 = 1. Use the linearization to determine the stabilityof the periodic orbit.