Answer
$${\text{linear}}$$
Work Step by Step
$$\eqalign{
& \frac{{dy}}{{dx}} = xy + {e^x} \cr
& {\text{subtract }}xy{\text{ from each side}} \cr
& \frac{{dy}}{{dx}} - xy = {e^x} \cr
& {\text{The equation can be written in the form }}\frac{{dy}}{{dx}} + P\left( x \right)y = Q\left( x \right)\,\,\,\left( {{\text{linear form}}} \right), \cr
& {\text{the given equation is linear}} \cr
& \cr
& {\text{The equation cannot be written in the form }}\frac{{dy}}{{dx}} = \frac{{p\left( x \right)}}{{q\left( y \right)}} \cr
& {\text{ then}}{\text{, the given equation is not separable}} \cr
& \cr
& {\text{linear}} \cr} $$
