(i)[4]
Write $\dfrac{1}{x^2(2x + 1)}$ as $\dfrac{A}{x^2} + \dfrac{B}{x} + \dfrac{C}{2x + 1}$.
(ii)[7]
The variables $x$ and $y$ satisfy the differential equation $y = x^2(2x + 1)\dfrac{dy}{dx}$, and $y = 1$ when $x = 1$. Solve the differential equation and determine the exact value of $y$ at $x = 2$. Give your answer for $y$ in a form that does not include logarithms.