| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | First order differential equations (integrating factor) |
| Type | Standard linear first order - variable coefficients |
| Difficulty | Standard +0.3 This is a standard integrating factor question requiring division by x to get standard form, finding μ = x^5, and integrating (ln x)x^4 by parts. While it involves multiple steps and integration by parts, it follows a completely routine procedure taught in FP2 with no novel insight required, making it slightly easier than average. |
| Spec | 4.10c Integrating factor: first order equations |
Find the general solution of the differential equation
$$x \frac{dy}{dx} + 5y = \frac{\ln x}{x}, \quad x > 0,$$
giving your answer in the form $y = f(x)$. [8]
\hfill \mbox{\textit{Edexcel FP2 Q3 [8]}}