3 The differential equation
$$\frac { 2 } { y } - \frac { x } { y ^ { 2 } } \frac { \mathrm {~d} y } { \mathrm {~d} x } = \frac { 1 } { x ^ { 2 } }$$
is to be solved subject to the condition \(y = 1\) when \(x = 1\).
- Show that \(y = \frac { 1 } { u }\) transforms the differential equation into
$$x \frac { \mathrm {~d} u } { \mathrm {~d} x } + 2 u = \frac { 1 } { x ^ { 2 } } .$$
- Find \(y\) in terms of \(x\).