Consider the differential equation y' = -18 + 11x -x2.
(a) Find the equilibria (i.e. constant solutions).
(b) By analyzing the sign of dy/dt around the equilibria,determine whether each equilibrium solution is stable, unstable, orneither.
(c) Find an explicit general solution to the equation.
(d) Graph the equilibrium solutions, as well as somenon-constant solution curves, verifying visually the stabilityproperties determined in (b).
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