Answer
$$y= \frac{1}{2}+ce^{-x^2}$$
Work Step by Step
Given $$ \frac{dy}{dx}+2xy=x$$
Since
\begin{align*}
\mu(x)&=e^{\int 2xdx}\\
&=e^{x^2}
\end{align*}
Then
\begin{align*}
y\mu(x)&=\int \mu(x) q(x)dx\\
e^{x^2}y&=\int xe^{x^2}dx\\
&=\frac{1}{2}e^{x^2}+c
\end{align*}
Hence $$y= \frac{1}{2}+ce^{-x^2}$$
