(a)[2]
Express $\frac{2}{1 - 9y^2}$ using partial fractions.
(b)[6]
The variables $x$ and $y$ are linked by the differential equation $2\cos^2(3x)\,\frac{dy}{dx} = 1 - 9y^2$, with $y = 0$ when $x = \frac{\pi}{12}$. Solve the differential equation and write $y$ in terms of $x$.