Solve the differential equation \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 y } { 3 \left( x ^ { 2 } - 1 \right) }\), given that \(y = 1\) when \(x = 3\). Show that the solution can be written as \(y ^ { 3 } = \frac { 2 ( x - 1 ) } { x + 1 }\).