This is a problem of section 2.3 of Engineering mathematics of Zill 7th international edition.
The problem is that "Find the general solution of the given differential equation and give the largest interval over which the general solution is defined." That's all written in problem.
My question is how to find the largest interval. For example, for $$ydx-4(x+y^6)dy=0,$$ I can find the general solution and note that it is linear.
The answer sheet says that the largest interval is $0<y<\infty$. I think that $y=0$ is impossible because in the process of finding solution we would work with $1/y$. But is it possible to choose $-\infty<y<0$?
Similarly, for $$(x^2 -1)dy/dx +2y=(x+1)^2,$$ can the largest interval be both $(-\infty,-1)$ and $(1, \infty)$?