OCR FP3 2007 January — Question 6

Exam BoardOCR
ModuleFP3 (Further Pure Mathematics 3)
Year2007
SessionJanuary
TopicFirst order differential equations (integrating factor)

6 The variables \(x\) and \(y\) satisfy the differential equation $$\frac { \mathrm { d } y } { \mathrm {~d} x } + 3 y = 2 x + 1$$ Find
  1. the complementary function,
  2. the general solution. In a particular case, it is given that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 0\) when \(x = 0\).
  3. Find the solution of the differential equation in this case.
  4. Write down the function to which \(y\) approximates when \(x\) is large and positive.