Past exam of the mathematical methods I course of the University of Oxford / 2016 / 9 / a / Solution

For $x\ne 0$, the integrating factor for $y^{\prime }-y/x=3$ can be taken as $1/x$ on either half-line. Thus $(y/x{)}^{\prime }=3/x$, givingThe arbitrary constant may differ on the disconnected domains $x>0$ and $x<0$.