CAIE P3 2021 March — Question 4

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2021
SessionMarch
TopicFirst order differential equations (integrating factor)

4 The variables \(x\) and \(y\) satisfy the differential equation $$( 1 - \cos x ) \frac { \mathrm { d } y } { \mathrm {~d} x } = y \sin x$$ It is given that \(y = 4\) when \(x = \pi\).
  1. Solve the differential equation, obtaining an expression for \(y\) in terms of \(x\).
  2. Sketch the graph of \(y\) against \(x\) for \(0 < x < 2 \pi\).