5. (a) Find, in terms of \(k\), the general solution of the differential equation $$\frac { \mathrm { d } ^ { 2 } x } { \mathrm {~d} t ^ { 2 } } + 4 \frac { \mathrm {~d} x } { \mathrm {~d} t } + 3 x = k t + 5 , \text { where } k \text { is a constant and } t > 0 .$$ For large values of \(t\), this general solution may be approximated by a linear function.
(b) Given that \(k = 6\), find the equation of this linear function.(2)(Total 9 marks)