AQA C4 2011 June — Question 8

Exam BoardAQA
ModuleC4 (Core Mathematics 4)
Year2011
SessionJune
TopicPartial Fractions
TypePartial fractions for differential equations

8
  1. Express \(\frac { 1 } { ( 3 - 2 x ) ( 1 - x ) ^ { 2 } }\) in the form \(\frac { A } { 3 - 2 x } + \frac { B } { 1 - x } + \frac { C } { ( 1 - x ) ^ { 2 } }\).
    (4 marks)
  2. Solve the differential equation $$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 \sqrt { y } } { ( 3 - 2 x ) ( 1 - x ) ^ { 2 } }$$ where \(y = 0\) when \(x = 0\), expressing your answer in the form $$y ^ { p } = q \ln [ \mathrm { f } ( x ) ] + \frac { x } { 1 - x }$$ where \(p\) and \(q\) are constants.