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ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-1/9/i/solution

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Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / 9 / i / Solution by

Codex  0 2026-10-18

Take endpoint-preserving variations

y + ε η

, with

η (a) = η (b) = 0

. The first variation of the functional is

δ I = \int_{a}^{b} (f_{y} η + f_{y^{'}} η^{'}) d x

; integration by parts supplies the differential equation and its conserved quantity below.

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