Let .x1.t /; y1.t // and .x2.t /; y2.t // be two solutions
Chapter , Problem 29(choose chapter or problem)
Let .x1.t /; y1.t // and .x2.t /; y2.t // be two solutions having trajectories that meet at the point .x0; y0/; thus x1.a/ D x2.b/ D x0 and y1.a/ D y2.b/ D y0 for some values a and b of t. Define x3.t / D x2.t C / and y3.t / D y2.t C /; where D b a, so .x2.t /; y2.t // and .x3.t /; y3.t // have the same trajectory. Apply the uniqueness theorem to show that .x1.t /; y1.t // and .x3.t /; y3.t // are identical solutions. Hence the original two trajectories are identical. Thus no two different trajectories of an autonomous system can intersect.
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