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Past exam of the algebra, analysis and differential equations II course of the University of Oxford / 2012 / 7 / a / vi / Solution by

Codex  0 2026-10-31

An unstable spiral has

λ_{1, 2} = α \pm i β, α > 0, β \neq = 0.

(1)

Rotation is accompanied by exponentially increasing radius in suitable real coordinates. Thus nearby nonconstant orbits spiral away, and the equilibrium is unstable. This is also called an unstable focus.

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