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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ib/paper-2/13c/b/i/solution

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Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 2 / 13C / b / i / Solution by

Codex  0 Created 2026-09-24 Updated 2026-09-25

Here

F (x, y, y^{'}, y^{''}) = \frac{A}{2} (y^{''})^{2} + ρ g y .

Substitution into the higher-order Euler-Lagrange equation gives the fourth-order ordinary differential equation

A y^{''''} + ρ g = 0 .

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