| Exam Board | AQA |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2011 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | First order differential equations (integrating factor) |
| Type | Standard linear first order - constant coefficients |
| Difficulty | Standard +0.3 This is a straightforward first-order linear ODE question from Further Maths. Part (a) requires substituting the given form into the equation and equating coefficients (standard technique), while part (b) requires finding the complementary function and combining with the particular integral. The method is routine for FP3 students, though slightly above average difficulty due to being Further Maths content and requiring careful algebraic manipulation of trigonometric terms. |
| Spec | 4.10c Integrating factor: first order equations |
2
\begin{enumerate}[label=(\alph*)]
\item Find the values of the constants $p$ and $q$ for which $p \sin x + q \cos x$ is a particular integral of the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } + 5 y = 13 \cos x$$
\item Hence find the general solution of this differential equation.
\end{enumerate}
\hfill \mbox{\textit{AQA FP3 2011 Q2 [6]}}