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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/2025/paper-1/7/a/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 / 2025 / Paper 1 / 7 / a / Solution by

Codex  0 2026-10-18

v = y - 1

turns the first-order linear differential equation into

v^{'} = v

. Its general solution is

v = C e^{x}

, so

y = 1 + C e^{x}

. The initial condition gives

C = - 1

, hence

y (x) = 1 - e^{x}, y (1) = 1 - e .

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