 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/i/solution

4 r^{2} + 8 r + 5 = 0,

r = - 1 \pm i /2

. Taking real and imaginary parts of the corresponding exponential functions gives the real general solution

y_{h} (x) = e^{- x} (A cos \frac{x}{2} + B sin \frac{x}{2}), A, B \in R .

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