 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/discrete-mathematics-continuous-mathematics-and-probability-resit/5/a/ii/solution

y_{p} = a sin x + b cos x

. Substitution gives

4 y_{p}^{''} + 8 y_{p}^{'} + 5 y_{p} = (a - 8 b) sin x + (8 a + b) cos x .

Matching coefficients requires

a - 8 b = 1

and

8 a + b = 8

, so

a = 1

and

b = 0

y (x) = sin x + e^{- x} (A cos \frac{x}{2} + B sin \frac{x}{2}) .

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