THEOREM 1 Existence and Uniqueness of Solutions Suppose that both the function f(x, y) and its partial derivative Dy f(x, y) are continuous on some rectangle R in the xy-plane that contains the point (a, b) in its interior. Then, for some open interval I containing the point a, the initial value problem dy dx 13. has one and only one solution that is defined on the interval I. In Problems 11 through 20, determine whether Theorem 1 does or does not guarantee existence of a solution of the given initial value problem. If existence is guaranteed, determine whether Theorem 1 does or does not guarantee uniqueness of that so- lution. = f(x, y), y(a) = b dy dx = 3/y; y(0) = 1 (9)

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