Answer
$$y= x^2+2x.$$
Work Step by Step
This is a linear equation and has the integrating factor as follows $$\alpha(x)= e^{\int P(x)dx}=e^{ -\int \frac{1}{x} dx}=e^{-\ln x}= \frac{1}{x} .$$
Now the general solution is
\begin{align}
y& =\alpha^{-1}(x)\left( \int\alpha(x) Q(x)dx +C\right)\\
& =x\left( \int dx+C\right)\\
& =x\left( x+C\right)\\
& =x^2+Cx \end{align}
Since, $y(1)=3$, then $C=2$
Thus, the general solution is:
$$y= x^2+2x.$$
