| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | First order differential equations (integrating factor) |
| Type | Substitution reducing to first order linear ODE |
| Difficulty | Challenging +1.2 This is a structured Further Maths question on Bernoulli equations requiring a given substitution, then applying integrating factor method. Part (a) is routine verification using chain rule. Part (b) is standard integrating factor technique with ∫tan x dx. The substitution is provided rather than requiring students to identify it independently, and each step is clearly signposted, making this moderately above average but not exceptionally challenging for FP2 students. |
| Spec | 4.10a General/particular solutions: of differential equations4.10c Integrating factor: first order equations |
\begin{enumerate}[label=(\alph*)]
\item Show that the transformation $z = y^{\frac{1}{2}}$ transforms the differential equation
$$\frac{dy}{dx} - 4y \tan x = 2y^{\frac{1}{2}}$$ [I]
into the differential equation
$$\frac{dz}{dx} - 2z \tan x = 1$$ [II]
\item Solve the differential equation (II) to find $z$ as a function of $x$. [6]
\item Hence obtain the general solution of the differential equation (I). [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q7 [7]}}