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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/2016/paper-2/8/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 / 2016 / Paper 2 / 8 / Solution by

Codex  0 2026-10-18

The characteristic equation is

(r - 1)^{2} = 0

, so the repeated-root constant-coefficient differential equation gives the general solution

y = (A + B x) e^{x}

. The first boundary condition gives

A = 0

, and the second gives

B π e^{π} = π e^{π}

, hence

B = 1

. Therefore

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

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