Answer
$$ y = x+\ln |x| +2 $$
Work Step by Step
Given
$$ \frac{dy}{dx}= 1+ \frac{1}{x} ,\ \ \ \ \ \ y(1)=3 $$
Then
\begin{align*}
y&= \int \left( 1+ \frac{1}{x} \right) dx\\
&= x+\ln |x| +c
\end{align*}
At $x= 1$ , $y= 3 $, then
$$ 3 =1+c\ \ \ \Rightarrow \ \ c= 2$$
Hence
$$ y = x+\ln |x| +2 $$
