| Exam Board | OCR |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | First order differential equations (integrating factor) |
| Type | Standard linear first order - variable coefficients |
| Difficulty | Standard +0.8 This is a first-order linear ODE requiring integrating factor method (standard FP3 technique), followed by applying a boundary condition and asymptotic analysis. While the method is standard, the integration involves products of polynomial and trigonometric functions requiring integration by parts, and the question tests multiple skills across three parts. This is moderately challenging for Further Maths but not exceptional. |
| Spec | 4.10c Integrating factor: first order equations |
\begin{enumerate}[label=(\roman*)]
\item Find the general solution of the differential equation
$$\frac{dy}{dx} - \frac{y}{x} = \sin 2x,$$
expressing $y$ in terms of $x$ in your answer. [6]
In a particular case, it is given that $y = \frac{2}{\pi}$ when $x = \frac{1}{4}\pi$.
\item Find the solution of the differential equation in this case. [2]
\item Write down a function to which $y$ approximates when $x$ is large and positive. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR FP3 Q5 [9]}}