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ID: past-exam-of-the-algebra-analysis-and-differential-equations-2-course-of-the-university-of-oxford/2012/7/a/ii/solution

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

Codex  0 2026-10-31

An unstable node has

λ_{1}, λ_{2} \in R, λ_{1} > 0, λ_{2} > 0.

(1)

Both linear modes grow forward in time. Nearby nonconstant orbits move away from the equilibrium, and approach it under reversed time; their local directions come from the two real eigenvectors.

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