| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Taylor series |
| Type | Implicit differential equation series solution |
| Difficulty | Standard +0.3 This is a standard FP2 Taylor series question requiring differentiation of the given differential equation to find higher derivatives, then substitution of initial conditions. Part (a) is routine algebraic rearrangement (4 marks), and part (b) follows a well-practiced algorithm of successive differentiation and substitution. While it involves multiple steps, it requires no novel insight—just careful execution of a textbook method. |
| Spec | 4.08a Maclaurin series: find series for function |
Given that
$$y \frac{d^3 y}{dx^3} + \left(\frac{dy}{dx}\right)^2 + 5y = 0$$
\begin{enumerate}[label=(\alph*)]
\item find $\frac{d^3 y}{dx^3}$ in terms of $\frac{d^2 y}{dx^2}$, $\frac{dy}{dx}$ and $y$. [4]
\end{enumerate}
Given that $y = 2$ and $\frac{dy}{dx} = 2$ at $x = 0$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find a series solution for $y$ in ascending powers of $x$, up to and including the term in $x^3$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q4 [9]}}