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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/2024/paper-2/15/a/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 / 2024 / Paper 2 / 15 / a / ii / Solution by

Codex  0 2026-10-18

The characteristic equation factors as

m^{2} + 6 m + 5 = (m + 1) (m + 5) = 0.

The distinct characteristic roots therefore give the general solution

y (x) = C_{1} e^{- x} + C_{2} e^{- 5 x} .

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