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

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, or neither.

(c) Find an explicit general solution to the equation.

(d) Graph the equilibrium solutions, as well as some non-constant solution curves, verifying visually the stability properties determined in (b).

Expert Solution

Colby Messinger answered 2 years ago

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