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Suppose that the solution (x(t),y(t)) is defined for all t and that its trajectory has an apparent self-intersection. x 1 (a)=x 1 (a+p)=x 0 ,

Suppose that the solution (x(t),y(t)) is defined for all t and that its trajectory has an apparent self-intersection. x1(a)=x1(a+p)=x0 , y1(a)=y1(a+p)=y0. With p>0. with the solution x2(t) = x1(t+p), y2(t) = y1(t+p),And applying the uniqueness theorem, show x1(a+p) = x1(t), y1(a+p) = y1(t). For all t. That is, the solution is closed and has a period p.

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