Question: (a) Rewrite the second-order equation as a system of two first-order equations. (b) Draw the nullclines for the first-order system, labeled with appropriate arrows, and

(a) Rewrite the second-order equation as a system of two first-order equations.
(b) Draw the nullclines for the first-order system, labeled with appropriate arrows, and find the equilibria.
(c) Deduce whether the equilibrium points of the nonlinear system are stable, thereby determining the stability of the constant solutions of the second-order DE.
(d) Identify any periodic solutions and state whether they are limit cycles.

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