Maximum interval of existence for the ODE $\space y'=\frac{y}{x}$. ODE: $\space y'=\frac{y}{x}$
Its solution is $\space y=Cx$
Here, I think Maximum interval of existence of solution is $(-\infty,+\infty)$
Or it is $\space \mathbb{R} \setminus \{0\} \space$ (because, ODE is not defined for $\space x=0$)
Please, help me in finding right solution. (I'm confused!)

It is not $(-\infty, \infty)$ becasue of the reason you mentioned. It cannot be $\mathbb R \setminus \{0\}$ because this set is not an interval!. The correct answer is $(0,\infty)$ or $(-\infty,0)$.
