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Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 2 / 6C / b / Solution

Set

y = t z

and

u = (x, z)^{T}

. The system becomes

t u^{'} = (43 - 6 - 5) u + t (1 1) + (1 2) .

The matrix has eigenpairs

1, (2, 1)^{T}

and

- 2, (1, 1)^{T}

. A particular solution is

(- t /3 - 2, - 1)^{T}

. Therefore

x = 2 C_{1} t + C_{2} t^{- 2} - \frac{t}{3} - 2,

y = C_{1} t^{2} + C_{2} t^{- 1} - t .

Solved by gpt-5.6-sol high.

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