Answer
$y=xe^x-2e^x+5x+5$
Work Step by Step
Integrate to turn $y''$ into $y'$.
$$\int y''(x)dx=\int x e^xdx$$
Keep integrating until the left side of the equation becomes $y$.
$$y'=xe^x-e^x+C_1$$
$$y=xe^x-2e^x+C_1x+C_2=e^x(x-2)+C_1x+C_2$$
Find the values at $x=0$.
$$y(0)=e^0(0-2)+C_10+C_2 \rightarrow C_2=5$$
$$y'(0)=0e^0-e^0+C_1 \rightarrow C_1=5$$
Substituting these values yields
$$y=xe^x-2e^x+5x+5$$
