| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | First order differential equations (integrating factor) |
| Type | Standard linear first order - variable coefficients |
| Difficulty | Standard +0.8 This is a standard integrating factor question (part a) worth 6 marks, but parts (b) and (c) require deeper analysis of solution behavior and sketching, which elevates it above routine exercises. The integrating factor method itself is straightforward, but identifying invariant points and sketching the particular solution requires geometric insight into differential equations beyond mechanical computation, making it moderately challenging for Further Maths. |
| Spec | 4.10c Integrating factor: first order equations |
\begin{enumerate}[label=(\alph*)]
\item Find the general solution of the differential equation
$$\cos x \frac{dy}{dx} + (\sin x)y = \cos^3 x.$$ [6]
\item Show that, for $0 \leq x \leq 2\pi$, there are two points on the $x$-axis through which all the solution curves for this differential equation pass. [2]
\item Sketch the graph, for $0 \leq x \leq 2\pi$, of the particular solution for which $y = 0$ at $x = 0$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q6 [11]}}