OCR FP3 2012 January — Question 1

Exam BoardOCR
ModuleFP3 (Further Pure Mathematics 3)
Year2012
SessionJanuary
TopicFirst order differential equations (integrating factor)

1 The variables \(x\) and \(y\) are related by the differential equation $$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 x ^ { 2 } + y ^ { 2 } } { x y } .$$
  1. Use the substitution \(y = u x\), where \(u\) is a function of \(x\), to obtain the differential equation $$x \frac { \mathrm {~d} u } { \mathrm {~d} x } = \frac { 2 } { u } .$$
  2. Hence find the general solution of the differential equation (A), giving your answer in the form \(y ^ { 2 } = \mathrm { f } ( x )\).