| Exam Board | AQA |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2010 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Second order differential equations |
| Type | Standard non-homogeneous with trigonometric RHS |
| Difficulty | Standard +0.8 This is a standard Further Maths second-order differential equation requiring finding a particular integral by inspection/trial solution, then combining with the complementary function. While methodical, it requires knowledge of the auxiliary equation method and understanding of how to handle non-homogeneous equations—concepts beyond standard A-level and requiring multiple coordinated steps typical of FP3 material. |
| Spec | 4.10d Second order homogeneous: auxiliary equation method4.10e Second order non-homogeneous: complementary + particular integral |
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\begin{enumerate}[label=(\alph*)]
\item Find the value of the constant $k$ for which $k \sin 2 x$ is a particular integral of the differential equation
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + y = \sin 2 x$$
\item Hence find the general solution of this differential equation.
\end{enumerate}
\hfill \mbox{\textit{AQA FP3 2010 Q2 [7]}}