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Given the differential equation y' = 8y2 and y(0) = -1 and its next few implicit derivatives y" = 16y y' y = 16 (y)2 + 16y y" y4 48 y'y" + 16 y y Use the initial value "y(0) = -1" to find the value of "y'(0)", "y"(0)", "y"(0)", and "y4(0)", then plug them into the Taylor Series Polynomial formula.

Given the differential equation y' = 8y2 and y(0) = -1 and its next few implicit derivatives y" = 16y y' y = 16 (y)2 + 16y y" y4 48 y'y" + 16 y y Use the initial value "y(0) = -1" to find the value of "y'(0)", "y"(0)", "y"(0)", and "y4(0)", then plug them into the Taylor Series Polynomial formula.

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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Given the differential equation y' = 8y2 and y(0) = - 1 and its next few implicit derivatives y" = 16y y' %3D y"' = 16 (y')2 + 16y y" y = 48 y'y" + 16 y y"" Use the initial value "y(0) = -1" to find the value of "y'(0)", "y"(0)", "y"(0)", and "y (0)", then plug them into the Taylor Series Polynomial formula. A y(x) = 0 + O! 16 64 8. x' + 1! 32 + 3! + - | 2! 4! 8. x! + 1! 128 x2 + 128 x3 + 3! 384 B y(x) = 0 ... O! 2! 4! - 16 - 4352 © y(x) O! 8. x' + 112 r3 + ... 1! 2! 3! 4! - 128 x2 + 3072 x3 + 3! - 98304 Dy(x) = - 0 + x! + x+ +... O! 1! 2! 4! 128 x2 + 2! 2176 83968 ® y(x) = O! 8 x! +3 3! (E r+ + ... 1! 4! O y(x) = 0 + O! 960 480 x2 x! + 1! x + 3! + + ... 2! 4! +
Transcribed Image Text:Given the differential equation y' = 8y2 and y(0) = - 1 and its next few implicit derivatives y" = 16y y' %3D y"' = 16 (y')2 + 16y y" y = 48 y'y" + 16 y y"" Use the initial value "y(0) = -1" to find the value of "y'(0)", "y"(0)", "y"(0)", and "y (0)", then plug them into the Taylor Series Polynomial formula. A y(x) = 0 + O! 16 64 8. x' + 1! 32 + 3! + - | 2! 4! 8. x! + 1! 128 x2 + 128 x3 + 3! 384 B y(x) = 0 ... O! 2! 4! - 16 - 4352 © y(x) O! 8. x' + 112 r3 + ... 1! 2! 3! 4! - 128 x2 + 3072 x3 + 3! - 98304 Dy(x) = - 0 + x! + x+ +... O! 1! 2! 4! 128 x2 + 2! 2176 83968 ® y(x) = O! 8 x! +3 3! (E r+ + ... 1! 4! O y(x) = 0 + O! 960 480 x2 x! + 1! x + 3! + + ... 2! 4! +
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