 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2020/paper-1/13/b/i/solution

y = e^{r x}

r^{2} + 3 r + 3 = 0

r = - \frac{3}{2} \pm \frac{3}{2} i .

Taking real combinations of the two complex exponential solutions produces the general solution

y_{c} (x) = e^{- 3 x /2} (A cos \frac{3 x}{2} + B sin \frac{3 x}{2}) .

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