IAL 2021 June Q6

(a) Find the general solution of the differential equation

\begin{align*} \frac{\mathrm{d}^2y}{\mathrm{d}x^2} - 6\frac{\mathrm{d}y}{\mathrm{d}x} + 8y = 2x^2 + x \end{align*}

(8)

(b) Find the particular solution of this differential equation for which $y = 1$ and $\frac{\mathrm{d}y}{\mathrm{d}x} = 0$ when $x = 0$

(5)