Find \(\int x \sqrt { x ^ { 2 } + 3 } \mathrm {~d} x\).
(2 marks)
Solve the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { x \sqrt { x ^ { 2 } + 3 } } { \mathrm { e } ^ { 2 y } }$$
given that \(y = 0\) when \(x = 1\). Give your answer in the form \(y = \mathrm { f } ( x )\).