Since f(x, y) = 1 + y2 and ∂f/∂y = 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 + y2, y(0) = 0. y = even though x0 = 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).