IAL 2022 June Q4

(a) Determine the general solution of the differential equation

\begin{align*} \frac{\mathrm{d}y}{\mathrm{d}x} - 3y \tan x =\,& \mathrm{e}^{4x} \sec^3 x\\[2mm] \end{align*}

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

(5)

(b) Determine the particular solution for which $y = 4$ at $x = 0$

(2)