CAIE P3 2019 June — Question 7

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2019
SessionJune
TopicFirst order differential equations (integrating factor)

7 The variables \(x\) and \(y\) satisfy the differential equation \(\frac { \mathrm { d } y } { \mathrm {~d} x } = x \mathrm { e } ^ { x + y }\). It is given that \(y = 0\) when \(x = 0\).
  1. Solve the differential equation, obtaining \(y\) in terms of \(x\).
  2. Explain why \(x\) can only take values that are less than 1 .