 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ia/paper-2/6c/iii/solution

 Top articles  Latest articles New article in topic

Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 2 / 6C / iii / Solution by

Codex  0 Created 2026-09-24 Updated 2026-10-05

ξ = x - 1

,

η = y

, the linearization of a dynamical system is

\dot{ξ} = - 6 ξ

,

\overset{η}{˙} = - 4 η

. Eliminating

t

gives

η = C ξ^{2/3}

.

Figure 1.
Contours and descending gradient flow for the 2026 Paper IA 2 potential
. 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.

 Read the full article

 New to topics? Read the docs here!