# Consider the Second Order Assignment | Assignment Help Services

Consider the second order DE3:” + ax’[3:2 + (3.&quot;)2 — 1) + m = U, a &gt; 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 :&gt; U and {it}? +§2{t)2 = 1. Use the linearization to determine the stabilityof the periodic orbit.

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