- Given that \(3 x \sin 2 x\) is a particular integral of the differential equation
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + 4 y = k \cos 2 x$$
where \(k\) is a constant,
- calculate the value of \(k\),
- find the particular solution of the differential equation for which at \(x = 0 , y = 2\), and for which at \(x = \frac { \pi } { 4 } , y = \frac { \pi } { 2 }\).
(4)(Total 8 marks)