| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Second order differential equations |
| Type | Resonance cases requiring modified PI |
| Difficulty | Standard +0.8 This is a Further Maths FP2 question on second-order differential equations with repeated roots (auxiliary equation gives m=3 twice), requiring recognition that the standard particular integral fails and needs modification to te^(3t). The question involves finding complementary function, particular integral with the correct form, and applying initial conditions. While systematic, it requires understanding of the repeated root case and careful algebraic manipulation across multiple steps, placing it moderately above average difficulty. |
| Spec | 4.10e Second order non-homogeneous: complementary + particular integral |
\begin{enumerate}[label=(\alph*)]
\item Find the value of $z$ for which $z^{2e^x}$ is a particular integral of the differential equation
$$\frac{d^2 y}{dt^2} - 6 \frac{dy}{dt} + 9y = 6e^{3t}, \quad t \geq 0$$ [5]
\item Hence find the general solution of this differential equation. [3]
\end{enumerate}
Given that when $t = 0$, $y = 5$ and $\frac{dy}{dt} = 4$
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item find the particular solution of this differential equation, giving your solution in the form $y = f(t)$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q7 [13]}}