- Find, in terms of \(k\), where \(k\) is a positive integer, the general solution of the differential equation
$$( 1 + x ) \frac { \mathrm { d } y } { \mathrm {~d} x } + k y = x ^ { \frac { 1 } { 2 } } ( 1 + x ) ^ { 2 - k } , \quad x > 0$$
giving your answer in the form \(y = \mathrm { f } ( x )\).
(6)