| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2016 |
| Session | June |
| Marks | 12 |
| 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 application of the integrating factor method for first order linear ODEs. Part (i) involves constant coefficients with a standard exponential solution and limit evaluation, while part (ii) requires integration by parts but follows the same routine procedure. Both are textbook-standard exercises with no novel insight required, though slightly above average difficulty due to being Further Maths content. |
| Spec | 4.10a General/particular solutions: of differential equations4.10c Integrating factor: first order equations |
4. (i)
$$p \frac { \mathrm {~d} x } { \mathrm {~d} t } + q x = r \quad \text { where } p , q \text { and } r \text { are constants }$$
Given that $x = 0$ when $t = 0$
\begin{enumerate}[label=(\alph*)]
\item find $x$ in terms of $t$
\item find the limiting value of $x$ as $t \rightarrow \infty$\\
(ii)
$$\frac { \mathrm { d } y } { \mathrm {~d} \theta } + 2 y = \sin \theta$$
Given that $y = 0$ when $\theta = 0$, find $y$ in terms of $\theta$\\
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\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 2016 Q4 [12]}}