| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2004 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | First order differential equations (integrating factor) |
| Type | Standard linear first order - constant coefficients |
| Difficulty | Standard +0.3 This is a straightforward integrating factor question with standard steps: find IF = e^(2x), multiply through, integrate to get general solution, apply initial condition, then find minimum by differentiation. While it's Further Maths content, it's a textbook application of the method with no conceptual challenges, making it slightly easier than average overall. |
| Spec | 4.10c Integrating factor: first order equations |
\begin{enumerate}
\item (a) Find the general solution of the differential equation
\end{enumerate}
$$\frac { \mathrm { d } y } { \mathrm {~d} x } + 2 y = x$$
Given that $y = 1$ at $x = 0$,\\
(b) find the exact values of the coordinates of the minimum point of the particular solution curve,\\
(c) draw a sketch of this particular solution curve.\\
\hfill \mbox{\textit{Edexcel FP2 2004 Q7 [11]}}