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  3. consider the differential equation y' = -18 + 11x

Consider the differential equation y' = -18 + 11x - x2. (a) Find the equilibria (i.e. constant...

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Advance Math

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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