I was solving an exercise about differential equations, and i really don't get how can I determinate the maximal domain of solution. Example: $$(dy/dx) = x - y/(1+x), y(0) =-1$$
The solution is $(-1/(1+x))(1-((x^2)/2)-((x^3)/3))$, and the solution, is that de Imax (maximal domain of solution) is $] − 1, +∞[$. Why it isn't R\(-1)?
I think a maximal domain of solution is an interval (also called the interval of validity of the ODE) by definition, thus it is $I = (-1,+\infty)$.