| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2018 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differential equations |
| Type | Exponential growth/decay - approach to limit (dN/dt = k(N - N₀)) |
| Difficulty | Moderate -0.3 This is a standard first-order linear differential equation with separable variables requiring routine integration and application of initial conditions. The method is straightforward (separate variables, integrate, apply boundary condition, rearrange for y), though it requires careful algebraic manipulation with logarithms and exponentials. Slightly easier than average as it's a textbook example with no conceptual challenges. |
| Spec | 1.08k Separable differential equations: dy/dx = f(x)g(y) |
The variable $y$ satisfies the differential equation
$$2\frac{dy}{dx} = 5 - 2y, \quad \text{where } x \geqslant 0.$$
Given that $y = 1$ when $x = 0$, find an expression for $y$ in terms of $x$. [5]
\hfill \mbox{\textit{WJEC Unit 3 2018 Q15 [5]}}