Solve the following differential equations: r = r(1 r2), = 1. By considering the

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Solve the following differential equations:

˙r = r(1 − r2), ˙ θ = 1.

By considering the line segment  = {(x, y) ∈ ℜ2 : 0 ≤ x ≤∞}, find the Poincaré map for this system.

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