Edexcel FP2 2006 January — Question 2

Exam BoardEdexcel
ModuleFP2 (Further Pure Mathematics 2)
Year2006
SessionJanuary
TopicSecond order differential equations

  1. Find the general solution of the differential equation $$\frac { \mathrm { d } ^ { 2 } x } { \mathrm {~d} t ^ { 2 } } + 2 \frac { \mathrm {~d} x } { \mathrm {~d} t } + 5 x = 0$$
  2. Given that \(x = 1\) and \(\frac { \mathrm { d } x } { \mathrm {~d} t } = 1\) at \(t = 0\), find the particular solution of the differential equation, giving your answer in the form \(x = \mathrm { f } ( t )\).
  3. Sketch the curve with equation \(x = \mathrm { f } ( t ) , 0 \leq t \leq \pi\), showing the coordinates, as multiples of \(\pi\), of the points where the curve cuts the \(x\)-axis.
    (4)(Total 13 marks)