| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 14 |
| 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 differential equation with constant coefficients and polynomial forcing term, requiring auxiliary equation solution, particular integral by inspection/undetermined coefficients, and applying initial conditions. While methodical with multiple steps (8+5+1=14 marks), it follows a well-established algorithm taught in FP2 without requiring novel insight or particularly challenging algebra, 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
$$2\frac{d^2 y}{dt^2} + 7\frac{dy}{dt} + 3y = 3t^2 + 11t.$$ [8]
\item Find the particular solution of this differential equation for which $y = 1$ and $\frac{dy}{dt} = 1$ when $t = 0$. [5]
\item For this particular solution, calculate the value of $y$ when $t = 1$. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q7 [14]}}