Express \(\frac { 1 } { ( 2 x + 1 ) ( x + 1 ) }\) in partial fractions.
A curve passes through the point \(( 0,2 )\) and satisfies the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { y } { ( 2 x + 1 ) ( x + 1 ) }$$
Show by integration that \(y = \frac { 4 x + 2 } { x + 1 }\).
Section B (36 marks)