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