| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | First order differential equations (integrating factor) |
| Type | Applied/modelling contexts |
| Difficulty | Standard +0.3 This is a straightforward first-order linear differential equation requiring the standard integrating factor method. Part (a) involves routine manipulation to find the integrating factor (1/t), integration, and algebraic rearrangement to reach the given form. Part (b) is simple substitution to find the constant and evaluate. While this is Further Maths content, the technique is mechanical and well-practiced, making it slightly easier than an average A-level question overall. |
| Spec | 4.10c Integrating factor: first order equations |
\begin{enumerate}[label=(\alph*)]
\item Find the general solution of the differential equation
$$t \frac{dv}{dt} - v = t, \quad t > 0$$
and hence show that the solution can be written in the form $v = t(\ln t + c)$, where $c$ is an arbitrary constant. [6]
\item This differential equation is used to model the motion of a particle which has speed $v$ m s$^{-1}$ at time $t$ s. When $t = 2$ the speed of the particle is $3$ m s$^{-1}$. Find, to $3$ significant figures, the speed of the particle when $t = 4$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q2 [10]}}