Answer
${\text{False}}$
Work Step by Step
$$\eqalign{
& y' + xy = {e^x}y \cr
& {\text{The first step is express }}y'{\text{ as }}\frac{{dy}}{{dx}} \cr
& \frac{{dy}}{{dx}} + xy = {e^x}y \cr
& {\text{We can note that the differential equation cannot be written in}} \cr
& {\text{the form }}\frac{{dy}}{{dx}} + P\left( x \right)y = Q\left( x \right),{\text{ }} \cr
& {\text{Therefore}}{\text{, it is not a first - order linear differential equation}}{\text{.}} \cr
& {\text{The statement is}}{\text{ FALSE.}} \cr} $$
