(a) Verify that is a one-parameter family of solutions of the differential equation
(b) Since are continuous everywhere, the region R in Theorem 1.2.1 can be taken to be the entire xy-plane. Find a solution from the family in part (a) that satisfies y(0) =1. Then find a solution from the family in part (a) that satisfies y(0)= -1. Determine the largest interval I of definition for the solution of each initial-value problem.
(c) Determine the largest interval I of definition for the solution of the first-order initial-value problem y(0) =0. [Hint: The solution is not a member of the family of solutions in part (a).]
(reference theorem 1.2.1)
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