| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | First order differential equations (integrating factor) |
| Type | Standard linear first order - constant coefficients |
| Difficulty | Standard +0.3 This is a standard first-order linear differential equation requiring the integrating factor method, followed by routine calculus to find a minimum point. While it's a Further Maths topic (slightly elevating difficulty), the question follows a completely standard template with no novel insights required. The integrating factor is straightforward (e^{2x}), integration is routine, and finding the minimum is a standard application of dy/dx = 0. Slightly above average due to being FP2 content and requiring multiple connected steps, but well within expected textbook exercises. |
| Spec | 4.10c Integrating factor: first order equations |
\begin{enumerate}[label=(\alph*)]
\item Find the general solution of the differential equation
$$\frac{dy}{dx} + 2y = x.$$ [5]
Given that $y = 1$ at $x = 0$,
\item find the exact values of the coordinates of the minimum point of the particular solution curve, [4]
\item draw a sketch of this particular solution curve. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q30 [11]}}