The answer to “(a) Verify that y = tan (x + c) is a one-parameter family of solutions of the differential equation (b) Since f (x, y) = 1 + y2 and 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(0) = 0. Even though x0 = 0 is in the interval (?2, 2), explain why the solution is not defined on this interval.(c) Determine the largest interval I of definition for the solution of the initial-value problem in part (b).Reference : Theorem 1.2.1” is broken down into a number of easy to follow steps, and 108 words. The full step-by-step solution to problem: 30E from chapter: 1.2 was answered by , our top Calculus solution expert on 07/17/17, 09:41AM. This full solution covers the following key subjects: interval, solution, Solutions, theorem, part. This expansive textbook survival guide covers 109 chapters, and 4053 solutions. This textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10. A First Course in Differential Equations with Modeling Applications was written by and is associated to the ISBN: 9781111827052. Since the solution to 30E from 1.2 chapter was answered, more than 273 students have viewed the full step-by-step answer.