The differential equation governing the motion of a nonlinear system is [ddot{x}-0.5 dot{x}+x-0.1 x^{3}=0] (a) Determine the

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The differential equation governing the motion of a nonlinear system is

\[\ddot{x}-0.5 \dot{x}+x-0.1 x^{3}=0\]

(a) Determine the equilibrium points.

(b) Classify the equilibrium points and determine their stability.

(c) Sketch a trajectory in the phase plane corresponding to each equilibrium point.

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