Problem

(a) Show that a solution from the family in part (a) of Problem 31 that satisfies is...

(a) Show that a solution from the family in part (a) of Problem 31 that satisfies is y = 1/(2 - x).

(b) Then show that a solution from the family in part (a) of Problem 31 that satisfies is

(c) Are the solutions in parts (a) and (b) the same?

(reference problem 31)

(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).]