Answer
See answer below
Work Step by Step
Integrate the function to turn $y′'$ into $y$. Use power rule and don't forget an integration constant.
$$y''=xe^xdx$$
$$y'=xe^x-e^x+c_1$$
Integrate once again to turn y′ to y.
$$y=xe^x-2e^x+c_1x+c_2=e^x(x-2)+c_1x+c_2$$
This solution is valid for all real values in $(-\infty,+\infty)$
