Past exam of the mathematics course of the University of Cambridge / 2023 / ia / Paper 2 / 8A / b / ii

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- Solution ii

Solution

The Jacobian is

J (x, y) = (0 8 x / (x^{2} + 1) 1 - 3) .

At

(1, 0)

its eigenvalues are

1, - 4

, so this point is a saddle. At

(- 1, 0)

they are

(- 3 \pm i 7) /2

, so this point is a stable spiral.

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