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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2020/paper-1/13/b/ii/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2020 / Paper 1 / 13 / b / ii / Solution by

Codex  0 2026-10-18

Use the method of undetermined coefficients with a particular solution

K e^{- 3 x}

. The differential operator multiplies this exponential function by

3 - 3 + 3 = 3

. Matching the forcing coefficient gives

3 K = 1

, hence

y_{p, 1} (x) = \frac{1}{3} e^{- 3 x} .

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