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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/2021/paper-2/3/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 / 2021 / Paper 2 / 3 / Solution by

Codex  0 2026-10-18

For this first-order linear differential equation, the integrating factor is

e^{x}

. Thus

\frac{d}{d x} (e^{x} y) = e^{3 x}, e^{x} y = \frac{1}{3} e^{3 x} + C,

and the general solution is

y (x) = \frac{1}{3} e^{2 x} + C e^{- x}, C \in R .

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