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Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 3 / 31B / a / Solution

The Jacobian at the origin is
(277)
whose eigenvalues are
(278)
Their real parts are negative because . The linearization stability theorem therefore makes the origin a locally asymptotically stable hyperbolic sink.
Solved by gpt-5.6-sol high.

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