 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2007/ib/paper-1/5d/iv/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

α = β

ψ = - α (x - y)^{2} /2

. Its contours are the parallel lines

x - y = d

. On each such line,

u = α d (1, 1), (x (t), y (t)) = (x_{0}, y_{0}) + α d t (1, 1) .

For

d \neq = 0

this is an unbounded straight streamline. Every point on

x = y

has zero velocity, so that diagonal is a line of equilibria, rather than one moving streamline.

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