Hey everyone, I've been trying to solve this differential equation for 2 days and I haven't gotten any closer to the answer. If someone could help that would be amazing, thank you. Here it is:

$\displaystyle xy' + y = y^2$

$\displaystyle y(1)=-11$

I've tried manipulating it to get y and dy on one side, and x and dx on the other side, and then integrating but that didn't work. I was left with:

$\displaystyle cx = y^2 - y$ where c is a constant. but i can't do anything from there.

I also tried doing $\displaystyle xy = \int y^2 dy$ where x is the constant of integration, but again, that didn't work out.

Can someone please help me?

Thank you,

CenturionMonkey