1.52: Show that

4PM1/1/November/2025 — Question 6 · 8 marks

y=e4xcos3xy = \mathrm{e}^{4x} \mathrm{cos} 3x
Show that
d2ydx2+Ay=BdydxwhereAandB are integers to be found.\frac{\mathrm{d}^{2}y}{\mathrm{d}x^2} + Ay = B \frac{\mathrm{d}y}{\mathrm{d}x} \quad \mathrm{where} A \mathrm{and} B \text{ are integers to be found.}
(8)