Solve the initial value problem $y′=(x+y−2)^2$?

Question

I don't usually have problems with solving ODEs but somehow I can't solve this one. I know that I have to substitute with $u$ and $u'$ but that's it...

Answer 1

Hint

Substitute $z=x+y-2=$ and $z'=y'+1$

Then solve $$z'-1=z^2$$ $$\int \frac {dz}{z^2+1}=x+K$$