5 It is given that \(y\) satisfies the differential equation
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + 2 \frac { \mathrm {~d} y } { \mathrm {~d} x } + 5 y = 8 \sin x + 4 \cos x$$
- Find the value of the constant \(k\) for which \(y = k \sin x\) is a particular integral of the given differential equation.
- Solve the differential equation, expressing \(y\) in terms of \(x\), given that \(y = 1\) and \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 4\) when \(x = 0\).
(8 marks)