| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | First order differential equations (integrating factor) |
| Type | Standard linear first order - variable coefficients |
| Difficulty | Standard +0.8 This is a standard integrating factor question from Further Maths FP2, requiring identification of P(x) = 2cot(2x), calculation of the integrating factor e^(∫2cot(2x)dx) = sin(2x), and integration of sin(2x)·sin(x) which needs a product-to-sum identity. While methodical, it involves multiple non-trivial steps including trigonometric integration that goes beyond routine A-level, placing it moderately above average difficulty. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=14.10c Integrating factor: first order equations |
Find the general solution of the differential equation
$$\frac{dy}{dx} + 2y \cot 2x = \sin x, \quad 0 < x < \frac{\pi}{2},$$
giving your answer in the form $y = f(x)$.
[7]
\hfill \mbox{\textit{Edexcel FP2 Q37 [7]}}