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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2022

Paper 4

Differentiate
$$
Q=f-\left(f_{y'}-\frac d{dx}f_{y''}\right)y'-f_{y''}y''.
$$
The product rule cancels all terms except
$$
Q'=y'\left(f_y-\frac d{dx}f_{y'}+\frac{d^2}{dx^2}f_{y''}\right)+f_x.
$$
On an extremal with no explicit $x$ dependence both terms vanish, proving the stated conserved quantity.


Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 4 / 13D / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 4 / 13D / b / Solution

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Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 4 / 13D / b / Solution

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