You can't obtain, by integrating both sides of . This is because,
The highlighted integrations could not be evaluated beacause they contain two variables whose relation we don't know.
But instead try,
Dividing by y,
Now use the substitution,
Hope you could countinue from here.
left side is the complete differential or whatever it is called in English, so we can integrate it. of course, there is a propability that i am wrong or making silly mistake, but i use this very often and so far i has been correct