CAIE P3 2016 June — Question 6

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2016
SessionJune
TopicFirst order differential equations (integrating factor)

6 The variables \(x\) and \(\theta\) satisfy the differential equation $$( 3 + \cos 2 \theta ) \frac { \mathrm { d } x } { \mathrm {~d} \theta } = x \sin 2 \theta$$ and it is given that \(x = 3\) when \(\theta = \frac { 1 } { 4 } \pi\).
  1. Solve the differential equation and obtain an expression for \(x\) in terms of \(\theta\).
  2. State the least value taken by \(x\).