With[{δ = 1*^-11},
     f = y /. First @ NDSolve[{y'[x] == y[x]^2 - y[x]^3, y[0] == δ},
                              y, {x, 0, 2/δ}]];

f["Domain"][[1, -1]]
   9.846458146821846*^10