Answer
$y = C{e^{\ln \left| x \right|}} - 3$
Work Step by Step
$$\eqalign{
& xy' = y + 3 \cr
& {\text{Write }}y'{\text{ as }}\frac{{dy}}{{dx}} \cr
& x\frac{{dy}}{{dx}} = y + 3 \cr
& {\text{Divide both sides by }}x \cr
& \frac{{dy}}{{dx}} = \frac{{y + 3}}{x} \cr
& {\text{Separate the variables}} \cr
& \frac{{dy}}{{y + 3}} = \frac{{dx}}{x} \cr
& {\text{Integrate both sides of the equation}} \cr
& \int {\frac{{dy}}{{y + 3}}} = \int {\frac{{dx}}{x}} \cr
& \ln \left| {y + 3} \right| = \ln \left| x \right| + k \cr
& {\text{solve for }}y \cr
& {e^{\ln \left| {y + 3} \right|}} = {e^{\ln \left| x \right| + k}} \cr
& y + 3 = {e^{\ln \left| x \right|}}{e^k} \cr
& {\text{Let 10}}k = C \cr
& y + 3 = C{e^{\ln \left| x \right|}} \cr
& y = C{e^{\ln \left| x \right|}} - 3 \cr} $$
