| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Second order differential equations |
| Type | Asymptotic behavior for large values |
| Difficulty | Standard +0.8 This is a standard second-order linear ODE with constant coefficients and a sinusoidal forcing term, requiring complementary function (complex roots), particular integral (trial solution method), and asymptotic analysis. While methodical, it demands fluency with multiple techniques and careful algebraic manipulation across 11 marks, placing it moderately above average difficulty for Further Maths. |
| Spec | 4.10d Second order homogeneous: auxiliary equation method4.10e Second order non-homogeneous: complementary + particular integral |
$$\frac{d^2 y}{dx^2} + 4\frac{dy}{dx} + 5y = 65 \sin 2x, \quad x > 0.$$
\begin{enumerate}[label=(\alph*)]
\item Find the general solution of the differential equation. [9]
\item Show that for large values of $x$ this general solution may be approximated by a sine function and find this sine function. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q27 [11]}}