Question: 1. Given the differential equation y' = y 3y + 2 (a) Find all equilibrium points, and sketch the phase line. (b) Classify the

1. Given the differential equation y' = y 3y + 2 (a) Find all equilibrium points, and sketch the phase line. (b) Classify the type of the equilibrium solutions (stable, semistable or unstable). = (c) If y y(t) represents the position of a particle, what are the velocity and acceleration of the particle in terms of y? In particular, what are the velocity and acceleration of the particle when it is found at y = 0? (d) Where does the particle have its largest/smallest value of its velocity/acceleration? (e) Sketch the equilibrium solutions along with a few integral curves above, below or between the equilibrium solutions. (f) Concavity of the integral curves are measured by acceleration as you found above. Are there any inflection levels, crossing through which the concavity of the integral curves changes?

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