Since f(x, y) = 1 + y² and ðf/ðy = 2y are continuous everywhere, the region R in Theorem 1.2.1 can be taken to be the entire xy-plane. Use the family of solutions in part (a) to find an explicit solution of the first-order initial-value problem y' = 1 + y?, y(0) = 0. y = y = tan(x+c) is solution to the equation Even though x, = 0 is in the interval (-2, 2), explain why the solution is not defined on this interval. Since tan(x) is discontinuous at x = + ), the solution is not defined on (-2, 2).

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