 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-3/39c/a/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Substitute the monochromatic wave

ϕ = e^{i (k x - ω t)}

(ik)^{9} = i k^{9}

, cancellation of the common exponential gives

- iω + i U k + \frac{i}{9} k^{9} = 0.

ω (k) = U k + \frac{k ^{9}}{9} .

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