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Given the differential equation y' = 4 cos(5y) and y(0) = 27 1. Use implicit derivatives to find "y" ", and "y"" 2. Use the initial value "y(0) = 2" to find the value of "y'(0)", "y"(0)", and "y"(0)". then plug them into the Taylor Series Polynomial formula. 2л x° + O! 20 x! + 1! - 100 x3 + (A) y(x) = x? + %3D ... 2! 3! By(x) 2л 87 x' + -40 - 200n x2 + r3 + ... 0! 1! 2! 3! - 360 x* + 3! -48 O y(x) - x0 + - ... O! 1! 2! - 100 y(x) 0! x' + 1! x2 + 2! ... 3! Ey(x) -20 x2 + r3 +... - O! 1! 2! 3! - 1600 y(x) 2л x° + O! 4 x! + 1! F x2 + 2! ... 3! + + +

Given the differential equation y' = 4 cos(5y) and y(0) = 27 1. Use implicit derivatives to find "y" ", and "y"" 2. Use the initial value "y(0) = 2" to find the value of "y'(0)", "y"(0)", and "y"(0)". then plug them into the Taylor Series Polynomial formula. 2л x° + O! 20 x! + 1! - 100 x3 + (A) y(x) = x? + %3D ... 2! 3! By(x) 2л 87 x' + -40 - 200n x2 + r3 + ... 0! 1! 2! 3! - 360 x* + 3! -48 O y(x) - x0 + - ... O! 1! 2! - 100 y(x) 0! x' + 1! x2 + 2! ... 3! Ey(x) -20 x2 + r3 +... - O! 1! 2! 3! - 1600 y(x) 2л x° + O! 4 x! + 1! F x2 + 2! ... 3! + + +

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Given the differential equation y' = 4 cos ( 5y) and y(0) = 2n 1. Use implicit derivatives to find "y"", and "y"" 2. Use the initial value "y(0) = 2" to find the value of "y'(0)", "y"(0)". and "y"(0)". then plug them into the Taylor Series Polynomial formula. A y(x) 2л x° + O! 20 x' + 1! - 100 x3 + x2 ... 2! 3! By(x) 2л -40 x2 - 200n x! + r3 + ... + 0! 1! 2! 3! - 48 - 360 © y(x) - x° + x' + + - ... O! 1! 2! 3! - 100 r3 D. y(x) 0! x' + 1! x2 + 2! -.. 3! E y(x) -20 + x2 + 3! r3 +... - O! 1! 2! - 1600 y(x) 2л x° + O! 4 x! + 1! F x2 + 2! ... 3! +
Transcribed Image Text:Given the differential equation y' = 4 cos ( 5y) and y(0) = 2n 1. Use implicit derivatives to find "y"", and "y"" 2. Use the initial value "y(0) = 2" to find the value of "y'(0)", "y"(0)". and "y"(0)". then plug them into the Taylor Series Polynomial formula. A y(x) 2л x° + O! 20 x' + 1! - 100 x3 + x2 ... 2! 3! By(x) 2л -40 x2 - 200n x! + r3 + ... + 0! 1! 2! 3! - 48 - 360 © y(x) - x° + x' + + - ... O! 1! 2! 3! - 100 r3 D. y(x) 0! x' + 1! x2 + 2! -.. 3! E y(x) -20 + x2 + 3! r3 +... - O! 1! 2! - 1600 y(x) 2л x° + O! 4 x! + 1! F x2 + 2! ... 3! +
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