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B3

Part of 1960 Putnam

Problems(1)

Putnam 1960 B3

Source: Putnam 1960

6/11/2022
The motion of the particles of a fluid in the plane is specified by the following components of velocity dxdt=y+2x(1−x2−y2),    dydt=−x.\frac{dx}{dt}=y+2x(1-x^2 -y^2),\;\; \frac{dy}{dt}=-x. Sketch the shape of the trajectories near the origin. Discuss what happens to an individual particle as t→∞t\to \infty, and justify your conclusion.
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