| Exam Board | AQA |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2012 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | First order differential equations (integrating factor) |
| Type | Standard linear first order - variable coefficients |
| Difficulty | Standard +0.3 This is a standard integrating factor question from Further Maths with straightforward application of the method. Part (a) requires identifying the integrating factor μ = x², multiplying through, and integrating ∫x²ln(x)dx using integration by parts. Part (b) applies a boundary condition to find the constant. While it's Further Maths content and requires integration by parts, it follows a completely routine procedure with no conceptual challenges, making it slightly easier than average overall. |
| Spec | 4.10c Integrating factor: first order equations |
4
\begin{enumerate}[label=(\alph*)]
\item By using an integrating factor, find the general solution of the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } + \frac { 2 } { x } y = \ln x$$
\item Hence, given that $y \rightarrow 0$ as $x \rightarrow 0$, find the value of $y$ when $x = 1$.
\end{enumerate}
\hfill \mbox{\textit{AQA FP3 2012 Q4 [10]}}