 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-2/14/b/i/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

Differentiate the equation for

f

with respect to

x

, commuting mixed partial derivatives for a sufficiently smooth solution. With

y = f_{x}

this gives

f_{x t} + f_{x} f_{xx} = k f_{xxx}, y_{t} + y y_{x} = k y_{xx} .

k > 0

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