| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2008 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | 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 requiring complementary function (solving auxiliary equation with distinct real roots) and particular integral (polynomial form). Part (b) requires understanding asymptotic behavior. While methodical, it's a multi-step Further Maths question requiring several techniques, placing it moderately above average difficulty. |
| Spec | 4.10d Second order homogeneous: auxiliary equation method4.10e Second order non-homogeneous: complementary + particular integral |
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $k$, the general solution of the differential equation
$$\frac{d^2x}{dt^2} + 4\frac{dx}{dt} + 3x = kt + 5, \text{ where } k \text{ is a constant and } t > 0.$$ (7)
For large values of $t$, this general solution may be approximated by a linear function.
\item Given that $k = 6$, find the equation of this linear function.(2)(Total 9 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 2008 Q5}}