CAIE P3 2014 November — Question 8

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2014
SessionNovember
TopicFirst order differential equations (integrating factor)

8 The variables \(x\) and \(y\) are related by the differential equation $$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 1 } { 5 } x y ^ { \frac { 1 } { 2 } } \sin \left( \frac { 1 } { 3 } x \right)$$
  1. Find the general solution, giving \(y\) in terms of \(x\).
  2. Given that \(y = 100\) when \(x = 0\), find the value of \(y\) when \(x = 25\).