IAL 2021 Jan Q6

(a) Determine the general solution of the differential equation

\begin{align*} \frac{\mathrm{d}^2y}{\mathrm{d}x^2} + 2\frac{\mathrm{d}y}{\mathrm{d}x} + 5y = 6\cos x \end{align*}

(7)

(b) Find the particular solution for which $y = 0$ and $\dfrac{\mathrm{d}y}{\mathrm{d}x} = 0$ at $x = 0$

(5)