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4. (a) Show that the solution of the initial value problem y = 1+y. y(0) = 0 is y(r) = tan z.

4. (a) Show that the solution of the initial value problem y = 1+y. y(0) = 0 is y(r) = tan z.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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4. (a) Show that the solution of the initial value problem y = 1+y. y(0) = 0 is y(r) = tan r. (b) Because y(z) = tan z is an odd function with y' (0) = 1, its Taylor series of the form y =1+ cr' + csr +czz" +... Substitute this series in y = 1+ y? and equate like powers of z to derive the following relations: (3c3 1, 5cs 2c3, Tey = 2cs + (cs), 9cg 207 + 2c3Cs, lle1 = 2c9 +2c3e7+ (cs)² (c) Conclude that 17 62 1382 tan z = 315 2835 155925 (d) Would you prefer to use the Maclaurin series formula to derive the tangent series in part (c)? Think about it!
Transcribed Image Text:4. (a) Show that the solution of the initial value problem y = 1+y. y(0) = 0 is y(r) = tan r. (b) Because y(z) = tan z is an odd function with y' (0) = 1, its Taylor series of the form y =1+ cr' + csr +czz" +... Substitute this series in y = 1+ y? and equate like powers of z to derive the following relations: (3c3 1, 5cs 2c3, Tey = 2cs + (cs), 9cg 207 + 2c3Cs, lle1 = 2c9 +2c3e7+ (cs)² (c) Conclude that 17 62 1382 tan z = 315 2835 155925 (d) Would you prefer to use the Maclaurin series formula to derive the tangent series in part (c)? Think about it!
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