Answer
$$ y=\sqrt{2(\ln x+2-\ln 3) }.$$
Work Step by Step
By separation of variables, we have
$$ y dy= x^{-1}dx $$
then by integration, we get
$$ \frac{1}{2}y^{2}=\ln x+c .$$
Now, since $y(3)=2$, then $c=2-\ln 3 $.
So the general solution is given by $$ y=\sqrt{2(\ln x+2-\ln 3) }.$$
