| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2007 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | First order differential equations (integrating factor) |
| Type | Standard linear first order - variable coefficients |
| Difficulty | Standard +0.3 This is a standard linear first-order differential equation requiring the integrating factor method. While it's a Further Maths topic (inherently harder), the question follows a routine procedure: divide by x to get standard form, find integrating factor x², multiply through, integrate cos(x)/x which requires integration by parts, and rearrange. The 8 marks reflect multiple steps rather than conceptual difficulty. Slightly above average due to the algebraic manipulation and integration by parts requirement, but still a textbook exercise with no novel insight needed. |
| Spec | 4.10c Integrating factor: first order equations |
\begin{enumerate}
\item Obtain the general solution of the differential equation
\end{enumerate}
$$x \frac { \mathrm {~d} y } { \mathrm {~d} x } + 2 y = \cos x , \quad x > 0$$
giving your answer in the form $y = \mathrm { f } ( x )$.\\
(Total 8 marks)\\
\hfill \mbox{\textit{Edexcel FP2 2007 Q1 [8]}}