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Given the differential equation y' = 3y e2 and y(0) = 4 1. Use implicit derivatives to find " y" ", " y"" 2. Use the initial value "y(0) = 4" to find the value of "y'(0)", "y"(0)", and "y"(0)", then plug them into the Taylor Series Polynomial formula.

Given the differential equation y' = 3y e2 and y(0) = 4 1. Use implicit derivatives to find " y" ", " y"" 2. Use the initial value "y(0) = 4" to find the value of "y'(0)", "y"(0)", and "y"(0)", then plug them into the Taylor Series Polynomial formula.

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' = 3y e2x and y(0) = 4 1. Use implicit derivatives to find " y"", " y"" 2. Use the initial value "y(0) = 4" to find the value of "y'(0)", "y"(0)", and "y"(0)", then plug them into the Taylor Series Polynomial formula. 4 x° + 0! 12 x' + 1! 36 x2 + 432 A) y(x) ... 2! 3! 864 3 + ... 4 12 B y(x) (B) 72 x2 + = - - 0! 1! 2! 3! 4 y(x) 0! 60 x2 + 12 372 x + + 2! ... 1! 3! 4 (D) y(x) + 3! r3 + ... | 0! 1! 2! y(x) 4 x° + 12 x! + 1! 27 x + (E) x2 - - - ... O! 2! 3! y(x) = 0! 36 x? + 12 108 x + 3! F | ... 1! 2! + +
Transcribed Image Text:Given the differential equation y' = 3y e2x and y(0) = 4 1. Use implicit derivatives to find " y"", " y"" 2. Use the initial value "y(0) = 4" to find the value of "y'(0)", "y"(0)", and "y"(0)", then plug them into the Taylor Series Polynomial formula. 4 x° + 0! 12 x' + 1! 36 x2 + 432 A) y(x) ... 2! 3! 864 3 + ... 4 12 B y(x) (B) 72 x2 + = - - 0! 1! 2! 3! 4 y(x) 0! 60 x2 + 12 372 x + + 2! ... 1! 3! 4 (D) y(x) + 3! r3 + ... | 0! 1! 2! y(x) 4 x° + 12 x! + 1! 27 x + (E) x2 - - - ... O! 2! 3! y(x) = 0! 36 x? + 12 108 x + 3! F | ... 1! 2! + +
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