Question: Consider the differential equation y = 3y (y + 3)(y-2). (a) Find the equilibrium solution(s). (b) Determine the interval of y values where the

Consider the differential equation y = 3y (y + 3)(y-2). (a) Find

Consider the differential equation y = 3y (y + 3)(y-2). (a) Find the equilibrium solution(s). (b) Determine the interval of y values where the solutions y(t) are either increasing or decreasing functions of t. (c) Sketch representative solution curves with various initial conditions, with at least one initial condition on each interval of increase/decrease. Label your axes. (d) On a different graph make a rough sketch of the solution to the initial value problem y = 3y (y + 3) (y-2), y(0) = 1.

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