$$\frac { \mathrm { d } y } { \mathrm {~d} x } + y \left( 1 + \frac { 3 } { x } \right) = \frac { 1 } { x ^ { 2 } } , \quad x > 0$$
- Verify that \(x ^ { 3 } \mathrm { e } ^ { x }\) is an integrating factor for the differential equation.
- Find the general solution of the differential equation.
- Given that \(y = 1\) at \(x = 1\), find \(y\) at \(x = 2\).
(3)(Total 10 marks)