| Exam Board | AQA |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2006 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | First order differential equations (integrating factor) |
| Type | Integrating factor with non-standard form |
| Difficulty | Standard +0.3 This is a straightforward integrating factor question from Further Maths. Part (a) requires verification by differentiation (routine), and part (b) involves standard integration of trigonometric functions. While it's Further Maths content, the method is mechanical and the integrations are standard, making it slightly easier than average overall. |
| Spec | 4.10c Integrating factor: first order equations |
3
\begin{enumerate}[label=(\alph*)]
\item Show that $\sin x$ is an integrating factor for the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } + ( \cot x ) y = 2 \cos x$$
\item Solve this differential equation, given that $y = 2$ when $x = \frac { \pi } { 2 }$.
\end{enumerate}
\hfill \mbox{\textit{AQA FP3 2006 Q3 [9]}}