| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2008 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Taylor series |
| Type | Differential equation given |
| Difficulty | Challenging +1.8 This is a Further Maths FP2 question requiring differentiation of an implicit differential equation using product rule and chain rule multiple times, then algebraic manipulation to reach a given result. While mechanically demanding with several steps, it's a 'show that' question with a clear target, making it more routine than open-ended proof questions at this level. |
| Spec | 4.10c Integrating factor: first order equations |
$$(x^2 + 1)\frac{d^2y}{dx^2} = 2y^2 + (1 - 2x)\frac{dy}{dx}$$ (I)
\begin{enumerate}[label=(\alph*)]
\item By differentiating equation (I) with respect to $x$, show that
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 2008 Q9}}