6 The differential equation \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + 4 y = \sin k x\) is to be solved, where \(k\) is a constant.
- In the case \(k = 2\), by using a particular integral of the form \(a x \cos 2 x + b x \sin 2 x\), find the general solution.
- Describe briefly the behaviour of \(y\) when \(x \rightarrow \infty\).
- In the case \(k \neq 2\), explain whether \(y\) would exhibit the same behaviour as in part (ii) when \(x \rightarrow \infty\).