| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differential equations |
| Type | Separable variables - standard (polynomial/exponential x-side) |
| Difficulty | Moderate -0.3 This is a straightforward separable variables question requiring standard technique: separate variables, integrate both sides (using power rule for √x and simple reciprocal for 1/y²), apply initial condition, and rearrange to make y the subject. While it requires multiple steps, the integration is routine and the method is a core C4 skill with no conceptual challenges. |
| Spec | 1.08k Separable differential equations: dy/dx = f(x)g(y) |
5. Given that $y = - 2$ when $x = 1$, solve the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = y ^ { 2 } \sqrt { x }$$
giving your answer in the form $y = \mathrm { f } ( x )$.\\
\hfill \mbox{\textit{OCR C4 Q5 [7]}}