 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-2/13/ii/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

The complementary characteristic roots are

- 1, - 2

. Substituting

A sin x + B cos x

(A - 3 B) sin x + (3 A + B) cos x

sin x - 3 cos x

. The initial conditions then require

C + D = 3

and

C + 2 D = 1

y = sin x - 3 cos x + 5 e^{- x} - 2 e^{- 2 x} .

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