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Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 2 / 14A / a / Solution

Substitution of

y = e^{- x}

gives

(x + λ + 1) e^{- x} - (x + λ) e^{- x} - e^{- x} = 0.

For a second solution

y = a x + b

, the ordinary differential equation reduces to

aλ - b = 0

. Taking

a = 1

gives the linearly independent solution

y_{1} = x + λ .

Solved by gpt-5.6-sol high.

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