| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Second order differential equations |
| Type | Solve via substitution then back-substitute |
| Difficulty | Challenging +1.3 This is a structured Further Maths question on second-order differential equations with a guided substitution. Part (a) requires careful but routine differentiation and algebraic manipulation (6 marks suggests multiple steps but no conceptual leaps). Part (b) involves solving a standard Euler-Cauchy equation, which is a core FP2 technique. Part (c) is trivial given the previous work. While this requires more sophistication than typical A-level questions and involves Further Maths content, the heavily scaffolded structure and standard techniques place it moderately above average but not exceptionally difficult. |
| Spec | 4.10e Second order non-homogeneous: complementary + particular integral |
\begin{enumerate}[label=(\alph*)]
\item Show that the transformation $y = xv$ transforms the equation
$$4x^2 \frac{d^2 y}{dx^2} - 8x \frac{dy}{dx} + (8 + 4x^2)y = x^4$$ [I]
into the equation
$$x^2 \frac{d^2 v}{dx^2} + 4v = x$$ [II] [6]
\item Solve the differential equation (II) to find $v$ as a function of $x$. [6]
\item Hence state the general solution of the differential equation (I). [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q7 [13]}}