Interpretation:
Verify the hypotheses of the existence and uniqueness theorem. To show
Concept Introduction:
The parametric curves traced by solutions of a differential equation are known as trajectories.
The geometrical representation of a collection of trajectories in a phase plane is called a phase portrait.
Existence and Uniqueness Theorem: For initial value problem
The corollary of Existence and Uniqueness Theorem: Different trajectories never intersect each other. If two trajectories intersect each other, then there is a possibility of the existence of the two solutions for the same point (intersecting point). This means trajectory moves in two directions from the same point which is not possible.
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Nonlinear Dynamics and Chaos
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