(a)[2]
Write $\frac{1}{4 - y^2}$ as a partial fraction expression.
(b)[6]
The variables $x$ and $y$ obey the differential equation $x\frac{dy}{dx} = 4 - y^2$, and $y = 1$ when $x = 1$. Solve the differential equation and obtain $y$ as a function of $x$.
(i)[2]
Decompose $\frac{1}{4 - y^2}$ into partial fractions.
(ii)[6]
The variables $x$ and $y$ obey the differential equation $x\frac{dy}{dx} = 4 - y^2$, and $y = 1$ when $x = 1$. Solve this differential equation to find an expression for $y$ in terms of $x$.