CAIE P3 2020 June — Question 8

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2020
SessionJune
TopicDifferential equations

8 A certain curve is such that its gradient at a point \(( x , y )\) is proportional to \(\frac { y } { x \sqrt { x } }\). The curve passes through the points with coordinates \(( 1,1 )\) and \(( 4 , \mathrm { e } )\).
  1. By setting up and solving a differential equation, find the equation of the curve, expressing \(y\) in terms of \(x\).
  2. Describe what happens to \(y\) as \(x\) tends to infinity.