4.
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + 4 \frac { \mathrm {~d} y } { \mathrm {~d} x } + 5 y = 65 \sin 2 x , x > 0$$
- Find the general solution of the differential equation.
- Show that for large values of \(x\) this general solution may be approximated by a sine function and find this sine function.
(3)(Total 12 marks)