14. (a) Given that \(y = \frac { 1 + \ln x } { x }\), show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { - \ln x } { x ^ { 2 } }\).
(b) Hence, solve the differential equation $$\frac { \mathrm { d } x } { \mathrm {~d} t } = \frac { x ^ { 2 } t } { \ln x } ,$$ given that \(t = 3\) when \(x = 1\).
Give your answer in the form \(t ^ { 2 } = g ( x )\), where \(g\) is a function of \(x\).