| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2004 |
| Session | June |
| Marks | 10 |
| 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 standard integrating factor question from FP2 where part (a) gives away the integrating factor, eliminating the main challenge of finding it. Parts (b) and (c) involve routine integration and applying initial conditions. While it requires multiple steps and careful algebra, the question provides significant scaffolding and follows a predictable template, making it slightly easier than average for A-level. |
| Spec | 4.10c Integrating factor: first order equations |
I'd be happy to help clean up mark scheme content, but I don't see any actual mark scheme text in your message. You've provided:
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Question 2:
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This appears to be incomplete. Could you please provide the full mark scheme content that you'd like me to convert and format?$$\frac { \mathrm { d } y } { \mathrm {~d} x } + y \left( 1 + \frac { 3 } { x } \right) = \frac { 1 } { x ^ { 2 } } , \quad x > 0$$
\begin{enumerate}[label=(\alph*)]
\item Verify that $x ^ { 3 } \mathrm { e } ^ { x }$ is an integrating factor for the differential equation.
\item Find the general solution of the differential equation.
\item Given that $y = 1$ at $x = 1$, find $y$ at $x = 2$.\\
(3)(Total 10 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 2004 Q2 [10]}}