| 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 +0.8 This is a first-order linear ODE requiring the integrating factor method with trigonometric functions. Students must recognize the standard form, find the integrating factor (sec x), and integrate sin(2x) which requires a double-angle identity. While systematic, it involves multiple non-trivial steps and careful algebraic manipulation, making it moderately challenging but still within standard Further Maths territory. |
| Spec | 4.10c Integrating factor: first order equations |
Find the general solution of the differential equation
$$\sin x \frac{dy}{dx} - y \cos x = \sin 2x \sin x$$
giving your answer in the form $y = f(x)$. [8]
\hfill \mbox{\textit{Edexcel FP2 Q3 [8]}}