First order differential equations (integrating factor)
10
Find the general solution of the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } + \frac { 2 y } { x } = \frac { x + 3 } { x ( x - 1 ) \left( x ^ { 2 } + 3 \right) } \quad ( x > 1 )$$
10
Find the particular solution for which \(y = 0\) when \(x = 3\)
Give your answer in the form \(y = \mathrm { f } ( x )\)