| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2012 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differential equations |
| Type | Separable variables - partial fractions |
| Difficulty | Standard +0.3 This is a straightforward separable differential equation requiring standard technique: separate variables, integrate both sides (partial fractions needed for the right side), apply initial condition, and rearrange for y. While it requires multiple steps and partial fractions, it follows a completely standard C4 procedure with no conceptual surprises, making it slightly easier than average. |
| Spec | 1.08k Separable differential equations: dy/dx = f(x)g(y) |
Question 6:
6
50
40
birth rate
30
(births per
1000
per year)
20
10
0
0 30 40 50 60 70 80
life expectancy (years)Solve the differential equation $\frac{dy}{dx} = \frac{y}{x(x+1)}$, given that when $x = 1$, $y = 1$. Your answer should express $y$ explicitly in terms of $x$. [8]
\hfill \mbox{\textit{OCR MEI C4 2012 Q6 [8]}}