Consider the autonomous equation dy/dt = f (y) where f (y) is continuously differentiable, and suppose we know that f (−1) = f (2) = 0.
(a) Describe all the possible behaviors of the solution y(t) that satisfies the initial condition y(0) = 1.
(b) Suppose also that f (y) > 0 for −1 < y<2. Describe all the possible behaviors of the solution y(t) that satisfies the initial condition y(0) = 1.
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