Question: Consider the differential equation dx/dt = x2. Find the equilibrium, graph the rate of change as a function of x, and draw the phase-line diagram.

Consider the differential equation dx/dt = x2. Find the equilibrium, graph the rate of change as a function of x, and draw the phase-line diagram. Would you consider the equilibrium to be stable or unstable?
As with discrete-time dynamical systems, equilibria can act strange when the slope of the rate-of-change function is exactly equal to the critical value of zero.

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