| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | First order differential equations (integrating factor) |
| Type | Standard linear first order - variable coefficients |
| Difficulty | Standard +0.8 This is a multi-part Further Maths question requiring integrating factor method, finding particular solutions, locating turning points, and sketching. While the integrating factor technique is standard, the question demands careful algebraic manipulation and complete analysis including optimization. The Further Maths context and extended multi-part nature place it moderately above average difficulty. |
| Spec | 1.07n Stationary points: find maxima, minima using derivatives4.10c Integrating factor: first order equations |
\begin{enumerate}[label=(\alph*)]
\item Find the general solution of the differential equation
$$x \frac{dy}{dx} + 2y = 4x^2$$ [5]
\item Find the particular solution for which $y = 5$ at $x = 1$, giving your answer in the form $y = f(x)$. [2]
\item Find the exact values of the coordinates of the turning points of the curve with equation $y = f(x)$, making your method clear. [???]
\item Sketch the curve with equation $y = f(x)$, showing the coordinates of the turning points. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q5 [12]}}