| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Topic | Second order differential equations |
| Type | Resonance cases requiring modified PI |
| Difficulty | Standard +0.8 This is a multi-part second order differential equation question from Further Maths requiring the method of undetermined coefficients for a resonance case (particular integral has same form as complementary function), followed by applying initial conditions and sketching. While systematic, it requires recognizing the resonance situation, careful differentiation of products, and handling multiple algebraic steps across 14 marks—moderately challenging for Further Maths students. |
| Spec | 4.10d Second order homogeneous: auxiliary equation method4.10e Second order non-homogeneous: complementary + particular integral |
\begin{enumerate}[label=(\alph*)]
\item Find the value of $\lambda$ for which $\lambda x \cos 3x$ is a particular integral of the differential equation
$$\frac{d^2 y}{dx^2} + 9y = -12 \sin 3x.$$ [4]
\item Hence find the general solution of this differential equation. [4]
The particular solution of the differential equation for which $y = 1$ and $\frac{dy}{dx} = 2$ at $x = 0$, is $y = g(x)$.
\item Find $g(x)$. [4]
\item Sketch the graph of $y = g(x)$, $0 \leq x \leq \pi$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q15 [14]}}