stability theory - What is steady state of differential equation? - Mathematics Stack Exchange

I am a beginner in Dynamical Systems and Stability Analysis. The theory starts from the definition of steady-state solution (equilibrium) of differential equations, but I cannot understand how the

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Stability of linear differential equations with periodic coefficients - Mathematics Stack Exchange

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Ordinary Differential Equations: Basics and Beyond

ordinary differential equations - Natural-Forced and Transient-SteadyState pairs of solutions - Mathematics Stack Exchange

In control theory, why do we linearize around the equilibrium for a nonlinear system? - Mathematics Stack Exchange