CAIE P3 2020 March — Question 6

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2020
SessionMarch
TopicFirst order differential equations (integrating factor)

6 The variables \(x\) and \(y\) satisfy the differential equation $$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 1 + 4 y ^ { 2 } } { \mathrm { e } ^ { x } }$$ It is given that \(y = 0\) when \(x = 1\).
  1. Solve the differential equation, obtaining an expression for \(y\) in terms of \(x\).
  2. State what happens to the value of \(y\) as \(x\) tends to infinity.