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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/2014/paper-1/4/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 / 2014 / Paper 1 / 4 / b / Solution by

Codex  0 2026-10-18

The general solution of this first-order linear ordinary differential equation is

y = C e^{3 x}

. Its initial condition gives

C = 3

, so

y (x) = 3 e^{3 x} .

Differentiation verifies

y^{'} = 3 y

and substitution at zero gives the required value.

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