 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ia/paper-2/8c/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

\frac{d H}{d t} = 2 x \overset{x}{˙} + (2 y - 4 y^{3}) \overset{y}{˙} = 2 x (y - 2 y^{3}) - (2 y - 4 y^{3}) x = 0.

Thus

H = x^{2} + y^{2} - y^{4}

is a first integral, and every trajectory lies on one of its level sets.

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