| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2024 |
| Session | February |
| Marks | 7 |
| 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 integrating factor method (standard Further Maths technique) followed by integration involving completing the square under a square root. The algebraic manipulation is moderately involved but follows established patterns. At 7 marks, it's a substantial question but uses well-practiced methods without requiring novel insight. |
| Spec | 4.10c Integrating factor: first order equations |
Find the general solution of the differential equation
$$x\frac{dy}{dx} - 2y = \frac{x^3}{\sqrt{4 - 2x - x^2}}$$
where $0 < x < \sqrt{5} - 1$ [7 marks]
\hfill \mbox{\textit{SPS SPS FM Pure 2024 Q12 [7]}}