Maximal Interval of Existence.
Solve the following ODE problem:
For every nonzero xo belonging to R, find the maximal interval of existence of the following initial problem:
x' = f(x) , x(0) = xo ,
where f: R{0} into R and f(x) = 1/x^2 . Guive proofs for your result. Skectch the region.