COnsider the initial value problem [at time tn = 1): s=f(x}=[zs)1e, cEIR, able-dd, m[1}=1'u {A} Find the largest set A C R where f is continuous, and the largest set E C R where f is continuously differentiable. (B) Using the Existence and Uniqueness Theorem from class, nd all possible initial values In at in = 1 for which the above initial value problem has a unique solution in some time interval around in = l. (C) For the remaining initial values :rI at in = 1, nd at least 1 different solutions. (D) Finally, consider the special case a. = 1, n = 3 and $1] = l}, namely the following initial value problem: i = [3: - 1}\"3, 3(1) = [1 Using {C}, explain why there is a. unique solution to this problem in some time interval around in = 1. Find that solution explicitly and nd the largest time interval I E R in which this solution malses sense. This solution can be extended to all of IR: nd an extension and explain why this extension is not unique. (Hint: recall (.31).)