CAIE P3 2016 March — Question 7

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2016
SessionMarch
TopicDifferential equations

7 The variables \(x\) and \(y\) satisfy the differential equation $$\frac { \mathrm { d } y } { \mathrm {~d} x } = x \mathrm { e } ^ { x + y }$$ and it is given that \(y = 0\) when \(x = 0\).
  1. Solve the differential equation and obtain an expression for \(y\) in terms of \(x\).
  2. Explain briefly why \(x\) can only take values less than 1 .