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Past exam of the mathematics course of the University of Cambridge / 2023 / ia / Paper 2 / 5A / a / Solution

Let

I (x) = exp (\int^{x} p (s) d s) .

The integrating factor identity

(I y)^{'} = I f

gives

y (x) = I (x)^{- 1} (C + \int^{x} I (t) f (t) d t) .

If

y_{1}, y_{2}

are distinct solutions, their difference is a nonzero homogeneous solution, so every solution is

y = y_{1} + C (y_{2} - y_{1}) .

Solved by gpt-5.6-sol high.

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