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Consider the autonomous differential equation dy/ dt = f(y) and suppose that y1 is a critical...

Consider the autonomous differential equation dy/ dt = f(y) and suppose that y1 is a critical point, i.e., f(y1) = 0.

Show that the constant equilibrium solution y = y1 is asymptotically stable if f 0 (y1) < 0 and unstable if f 0 (y1) > 0.

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