(a) Determine the maximal interval of existence for each of the following initial value problems:

(i) ˙ x = x4, x(0) = 1;

(ii) ˙ x = x2−1 2 , x(0) = 2;

(iii) ˙ x = x(x − 2), x(0) = 3.

(b) For what values of t0 and x0 does the initial value problem

˙ x = 2√x, x(t0) = x0, have a unique solution?