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Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 1 / 11E / c / Solution

For

h = f_{1} - f_{2}

,

h' = 1 + x (f_{1} + f_{2}) h

and

h (0) = 0

. On every compact subinterval the coefficient is continuous, so Gronwall inequality gives

h = 0

; hence equality holds throughout

[0, a)

.

Solved by gpt-5.6-sol high.

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