Express \(\frac { 3 } { ( y - 2 ) ( y + 1 ) }\) in partial fractions. [0pt]
[3]
Hence, given that \(x\) and \(y\) satisfy the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = x ^ { 2 } ( y - 2 ) ( y + 1 )$$
show that \(\frac { y - 2 } { y + 1 } = A \mathrm { e } ^ { x ^ { 3 } }\), where \(A\) is a constant.