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