Linear Algebra and Differential Equations
Unstable equilibrium refers to a state of balance in a system where any small perturbation or disturbance leads to a significant deviation from that equilibrium point. In this context, when the system is slightly disturbed, it moves away from the equilibrium instead of returning to it, indicating that the forces at play favor divergence rather than restoration. This concept is critical in understanding the behavior of systems described by first-order differential equations, particularly when assessing stability and the long-term behavior of solutions.
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