(Solution) - The second order linear DE mx bx kx -(2025 Original AI-Free Solution)

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The second-order linear DE mx + bx + kx = 0 models vibrations of a mass m attached to a spring with spring constant k and damping constant b.
For the nonlinear variations in Problems 17-20, use your intuition to decide whether the zero solution (x = z = 0) is stable or unstable. Check your intuition by transforming to a first-order system and linearizing.
x + x3 + x = 0