Consider the following differential equations. Determine if the Existence and Uniqueness Theorem does or does not guarantee existence and uniqueness of a solution of each of the following initial value problems.
I. y/x = sqrt(x − y), y(2) = 2
II. y/x = sqrt(x − y), y(2) = 1
III. y (y/x) = x − 1, y(0) = 1
IV. y (y/x) = x − 1, y(1) = 0