| Exam Board | WJEC |
|---|---|
| Module | Further Unit 4 (Further Unit 4) |
| Year | 2024 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | First order differential equations (integrating factor) |
| Type | Standard linear first order - variable coefficients |
| Difficulty | Challenging +1.2 This is a first-order linear ODE requiring identification of integrating factor (sec x), integration of standard trigonometric forms, and application of initial conditions. While it involves multiple steps and careful algebraic manipulation, the method is systematic and well-practiced in Further Maths syllabi. The trigonometric integration is moderately challenging but follows standard patterns, placing it above average difficulty but not requiring novel insight. |
| Spec | 4.10c Integrating factor: first order equations |
Given the differential equation
$$\cos x \frac{\mathrm{d}y}{\mathrm{d}x} + y \sin x = 4 \cos^2 x \sin x + 5$$
and $y = 3\sqrt{2}$ when $x = \frac{\pi}{4}$, find an equation for $y$ in terms of $x$. [9]
\hfill \mbox{\textit{WJEC Further Unit 4 2024 Q3 [9]}}