| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Year | 2013 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | First order differential equations (integrating factor) |
| Type | Standard linear first order - vector form |
| Difficulty | Standard +0.8 This is a vector differential equation requiring integrating factor method (standard technique) but with non-standard initial conditions involving dot and cross products that must be unpacked into component form. The mechanics context and vector manipulation elevate it above routine first-order DE questions, requiring careful interpretation and multi-step reasoning beyond textbook exercises. |
| Spec | 4.10b Model with differential equations: kinematics and other contexts |
Solve the differential equation $\frac{dr}{dt} - 2r = 0$ given that when $t = 0$, $r \cdot j = 0$ and $r \times j = i + k$.
(7 marks)
---\begin{enumerate}
\item Solve the differential equation
\end{enumerate}
$$\frac { \mathrm { d } \mathbf { r } } { \mathrm {~d} t } - 2 \mathbf { r } = \mathbf { 0 }$$
given that when $t = 0 , \mathbf { r } . \mathbf { j } = 0$ and $\mathbf { r } \times \mathbf { j } = \mathbf { i } + \mathbf { k }$.\\
\hfill \mbox{\textit{Edexcel M5 2013 Q1 [7]}}