 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2010/ia/paper-2/1a/iv/solution

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

The superposition principle applies because the recurrence operator is linear. Add the particular solutions from parts (ii) and (iii), then add the general homogeneous linear recurrence relation solution from part (i). This gives

y_{n} = A + B n + C (- 2)^{n} - \frac{n}{18} (- 2)^{n} + \frac{2 ^{n}}{4} .

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