| Exam Board | OCR |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 10 |
| 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 the integrating factor method (standard FP3 technique), but the integration of cos³x·sec x = cos²x requires a trigonometric identity and substitution. The particular solution is straightforward once the general solution is found. More challenging than routine C3/C4 integration due to the algebraic manipulation and being a Further Maths topic, but follows a well-defined method without requiring novel insight. |
| Spec | 4.10c Integrating factor: first order equations |
\begin{enumerate}[label=(\roman*)]
\item Find the general solution of the differential equation
$$\frac{dy}{dx} + y\tan x = \cos^3 x,$$
expressing $y$ in terms of $x$ in your answer. [8]
\item Find the particular solution for which $y = 2$ when $x = \pi$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR FP3 Q8 [10]}}