| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | First order differential equations (integrating factor) |
| Type | Standard linear first order - variable coefficients |
| Difficulty | Standard +0.8 This is a Further Maths FP2 question requiring recognition of the integrating factor method, manipulation of trigonometric expressions (sin 2x = 2sin x cos x), and integration involving sec x. While the technique is standard for FP2, the execution requires careful algebraic manipulation and the particular solution involves non-trivial evaluation at specific angles. The 10-mark allocation and multi-step nature place it moderately above average difficulty. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=14.10c Integrating factor: first order equations |
\begin{enumerate}[label=(\alph*)]
\item Find, in the form $y = f(x)$, the general solution of the equation
$$\frac{dy}{dx} = 2y \tan x + \sin 2x, \quad 0 < x < \frac{\pi}{2}$$ [6]
\end{enumerate}
Given that $y = 2$ at $x = \frac{\pi}{6}$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the value of $y$ at $x = \frac{\pi}{4}$, giving your answer in the form $a + k \ln b$,
where $a$ and $b$ are integers and $k$ is rational. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q5 [10]}}