| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2006 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Second order differential equations |
| Type | Verify particular integral form |
| Difficulty | Standard +0.8 This is a Further Maths FP2 question requiring verification of a particular integral by substitution, then finding the general solution and applying two boundary conditions. While the differentiation of the product 3x sin 2x requires careful application of product and chain rules, and the algebra involves trigonometric manipulation, this is a standard textbook exercise following a predictable method. It's moderately above average difficulty due to being Further Maths content with multiple computational steps, but doesn't require novel insight. |
| Spec | 4.10e Second order non-homogeneous: complementary + particular integral |
\begin{enumerate}
\item Given that $3 x \sin 2 x$ is a particular integral of the differential equation
\end{enumerate}
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + 4 y = k \cos 2 x$$
where $k$ is a constant,\\
(a) calculate the value of $k$,\\
(b) find the particular solution of the differential equation for which at $x = 0 , y = 2$, and for which at $x = \frac { \pi } { 4 } , y = \frac { \pi } { 2 }$.\\
(4)(Total 8 marks)\\
\hfill \mbox{\textit{Edexcel FP2 2006 Q1 [8]}}