Express \(\frac { 1 } { x ( 2 x + 3 ) }\) in partial fractions.
The variables \(x\) and \(y\) satisfy the differential equation
$$x ( 2 x + 3 ) \frac { \mathrm { d } y } { \mathrm {~d} x } = y$$
and it is given that \(y = 1\) when \(x = 1\). Solve the differential equation and calculate the value of \(y\) when \(x = 9\), giving your answer correct to 3 significant figures.