| 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 | Particular solution with initial conditions |
| Difficulty | Challenging +1.2 This is a standard second-order linear differential equation with constant coefficients and polynomial forcing term. Part (a) requires finding the complementary function (solving the auxiliary equation) and a particular integral (trying y = ax² + bx + c), which is methodical but involves several algebraic steps. Part (b) applies initial conditions to find constants. While this is Further Maths content making it inherently harder than standard A-level, it's a textbook example requiring no novel insight—just systematic application of the standard method taught in FP2. |
| Spec | 4.10e Second order non-homogeneous: complementary + particular integral |
\begin{enumerate}[label=(\alph*)]
\item Find the general solution of the differential equation $3\frac{d^2y}{dx^2} - \frac{dy}{dx} - 2y = x^2$ (8)
\item Find the particular solution for which, at $x = 0$, $y = 2$ and $\frac{dy}{dx} = 3$. (6)(Total 14 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 2008 Q3}}