# Math Help - Domain of an ODE

1. ## Domain of an ODE

I am not understanding how the domain is supposed to work. I know that x cannot be 0, but I'm confused about the interval. Looking at the direction field for the solution that goes through (-1,1), I see a parabola that seems to be bounded by x=-2 and x=0. What does this mean in terms of the domain?

$\frac{dy}{dx}=(1+x)(1+y)^2, \;\; y(-1)=1$

2. OK, perhaps I was being too vague? Is the domain x<0?

3. Alright, then I would just solve it:

$y(x)=-\frac{2+2x+x^2}{x(2+x)}$

Bingo: $x\notin\{0,-2\}$

4. Looks like I made an algebraic error, getting $y=-\frac{2}{x^2}-\frac{1}{x}-1$. So the domain would be -2<x<0, then? That would make sense with regards to the direction field.