| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Second order differential equations |
| Type | Particular solution with initial conditions |
| Difficulty | Standard +0.8 This is a standard second-order linear ODE with constant coefficients requiring auxiliary equation solution (complex roots giving e^{-t}(A cos t + B sin t)), finding a particular integral for the non-homogeneous term (2e^{-t}), then applying initial conditions. While methodical and multi-step (12 marks total), it follows a well-established algorithm taught in FP2 without requiring novel insight, 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 the general solution of the differential equation
$$\frac{d^2 y}{dt^2} + 2\frac{dy}{dt} + 2y = 2e^{-t}.$$ [6]
\item Find the particular solution that satisfies $y = 1$ and $\frac{dy}{dt} = 1$ at $t = 0$. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q31 [12]}}