Express \(\frac { 16 x } { ( 1 - 3 x ) ( 1 + x ) ^ { 2 } }\) in the form \(\frac { A } { 1 - 3 x } + \frac { B } { 1 + x } + \frac { C } { ( 1 + x ) ^ { 2 } }\).
Solve the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 16 x \mathrm { e } ^ { 2 y } } { ( 1 - 3 x ) ( 1 + x ) ^ { 2 } }$$
where \(y = 0\) when \(x = 0\).
Give your answer in the form \(\mathrm { f } ( y ) = \mathrm { g } ( x )\). [0pt]
[7 marks]