| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2022 |
| Session | June |
| Marks | 8 |
| Topic | Differential equations |
| Type | Separable variables - standard (polynomial/exponential x-side) |
| Difficulty | Standard +0.8 This is a separable differential equation requiring integration of both sides, application of an initial condition, and algebraic manipulation to reach the specified form. While the separation and integration are standard Further Maths techniques (integrating 1/(4-y²) requires partial fractions or recognition of an inverse tanh/inverse trig form, and integrating cot x is routine), the multi-step process, careful algebraic rearrangement to reach sec²x = g(y), and the 8-mark allocation indicate this is moderately challenging—above average difficulty but not requiring exceptional insight. |
| Spec | 1.08k Separable differential equations: dy/dx = f(x)g(y)4.10a General/particular solutions: of differential equations |
Solve the differential equation
$$2\cot x \frac{dy}{dx} = (4 - y^2)$$
for which $y = 0$ at $x = \frac{\pi}{3}$, giving your answer in the form $\sec^2 x = g(y)$. [8]
\hfill \mbox{\textit{SPS SPS FM Pure 2022 Q11 [8]}}