= Solution
Writing $\xi=x-1$, $\eta=y$, the <linearization of a dynamical system> is $\dot\xi=-6\xi$, $\dot\eta=-4\eta$. Eliminating $t$ gives $\eta=C\xi^{2/3}$.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ia/paper-2-gradient-flow.png]
{title=Contours and descending gradient flow for the 2026 Paper IA 2 potential}
{description=Contour lines of U equal x cubed minus 3x plus open parenthesis x plus 1 close parenthesis y squared are overlaid with the descending gradient field. The highlighted trajectory starts at open parenthesis 2 comma 1 close parenthesis and tends to the local minimum at open parenthesis 1 comma 0 close parenthesis; the other marked critical point is degenerate.}
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