| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2023 |
| Session | October |
| Marks | 5 |
| Topic | Differential equations |
| Type | Separable variables - partial fractions |
| Difficulty | Moderate -0.3 This is a straightforward separable variables question requiring separation, integration using partial fractions (standard A-level technique), and stating the general solution. While it involves multiple steps, each is routine for Further Maths students and follows a well-practiced algorithm with no novel insight required. |
| Spec | 1.08k Separable differential equations: dy/dx = f(x)g(y) |
2.
Given that $x \geqslant 2$, find the general solution of the differential equation
$$( 2 x - 3 ) ( x - 1 ) \frac { \mathrm { d } y } { \mathrm {~d} x } = ( 2 x - 1 ) y$$
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\hfill \mbox{\textit{SPS SPS FM Pure 2023 Q2 [5]}}