Edexcel FP2 — Question 7 14 marks

Exam BoardEdexcel
ModuleFP2 (Further Pure Mathematics 2)
Marks14
PaperDownload PDF ↗
TopicSecond order differential equations
TypeParticular solution with initial conditions
DifficultyStandard +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.
Spec4.10d Second order homogeneous: auxiliary equation method4.10e Second order non-homogeneous: complementary + particular integral

  1. Find the general solution of the differential equation $$2\frac{d^2 y}{dt^2} + 7\frac{dy}{dt} + 3y = 3t^2 + 11t.$$ [8]
  2. Find the particular solution of this differential equation for which \(y = 1\) and \(\frac{dy}{dt} = 1\) when \(t = 0\). [5]
  3. For this particular solution, calculate the value of \(y\) when \(t = 1\). [1]

\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]}}