| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | First order differential equations (integrating factor) |
| Type | Integrating factor with non-standard form |
| Difficulty | Standard +0.3 This is a straightforward integrating factor question where part (a) removes the challenge of finding the integrating factor by giving it directly. Students only need to verify it (routine differentiation/algebra), integrate both sides in part (b), and apply an initial condition in part (c). While integrating factors are a Further Maths topic, this question requires no problem-solving insight—just methodical application of the standard technique with integration by parts. |
| Spec | 4.10c Integrating factor: first order equations |
$$\frac{dy}{dx} + y\left(1 + \frac{3}{x}\right) = \frac{1}{x^2}, \quad x > 0.$$
\begin{enumerate}[label=(\alph*)]
\item Verify that $x^3e^x$ is an integrating factor for the differential equation. [3]
\item Find the general solution of the differential equation. [4]
\item Given that $y = 1$ at $x = 1$, find $y$ at $x = 2$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q25 [10]}}