OCR FP3 2011 June — Question 3

Exam BoardOCR
ModuleFP3 (Further Pure Mathematics 3)
Year2011
SessionJune
TopicSecond order differential equations

3 The variables \(x\) and \(y\) satisfy the differential equation $$\frac { \mathrm { d } y } { \mathrm {~d} x } + 4 y = 5 \cos 3 x$$
  1. Find the complementary function.
  2. Hence, or otherwise, find the general solution.
  3. Find the approximate range of values of \(y\) when \(x\) is large and positive.