IAL 2021 Oct Q4

(a) Determine the general solution of the differential equation

\begin{align*} (x + 1) \frac{\mathrm{d}y}{\mathrm{d}x} - xy =\,& \mathrm{e}^{3x} \qquad x > -1\\[2mm] \end{align*}

giving your answer in the form $y = \mathrm{f}(x)$ .

(7)

(b) Determine the particular solution of the differential equation for which $y = 5$ when $x = 0$ .

(2)