 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2006/ia/paper-2/6b/i/solution

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

U (s, y) = u (s, y + s)

. Holding

y

fixed while differentiating in

s

gives

U_{s} = u_{t} + u_{x}

, while

U_{y} = u_{x}

and

U_{yy} = u_{xx}

U_{s} = U_{yy} + F (s, y), F (s, y) = f (s, y + s) .

The moving coordinate follows the unit-speed advection, leaving the heat equation with a transformed source.

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