 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2011/paper-1/14/e/solution

Using the sine addition formula, combine the surviving modes:

y (x) = sin x - 3 cos x = 2 sin (x - π /3) .

2

and a phase delay

π /3

. The full general solution would add

C e^{- x / 3}

, but this exponential is periodic only for

C = 0

, so the displayed periodic solution is unique.

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