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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/b/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 / b / Solution by

Codex  0 2026-10-18

The general solution of the first-order linear differential equation is

y = 1 + C e^{x}

. The initial condition

y (0) = 1

gives

C = 0

, so the solution of this initial value problem is the constant function

y (x) = 1

. Thus

y (1) = 1

.

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