Answer
$$ y= x-\frac{1}{x}+10.$$
Work Step by Step
By separation of variables, we have
$$ dy=(1 + x^{-2} ) dx$$
then by integration, we get
$$ y=x-\frac{1}{x}+c .$$
Now, since $y(1)=10$, then $c=10$.
So the general solution is given by $$ y= x-\frac{1}{x}+10.$$
