For the system (2a) and (2b), show that any trajectory starting on the unit circle x² + y² = 1 will traverse the unit circle in a periodic solution. First introduce polar coordinates and rewrite the system as dr/dt = r(1 - r²) and -dθ/dt = -1.

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dx dt dy dt = y + x - x(x2+y2), = x + y - y(x2+y^2) (2a) (2b)