Assuming that the trajectory corresponding to a solution x = (t), y = (t), < t < ,of an
Chapter 9, Problem 28(choose chapter or problem)
Assuming that the trajectory corresponding to a solution x = (t), y = (t), < t < ,of an autonomous system is closed, show that the solution is periodic.Hint: Since the trajectory is closed, there exists at least one point (x0, y0) such that(t0) = x0, (t0) = y0 and a number T > 0 such that (t0 + T) = x0, (t0 + T) = y0. Showthat x = (t) = (t + T) and y = (t) = (t + T) is a solution, and then use the existenceand uniqueness theorem to show that (t) = (t) and (t) = (t) for all t.
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