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Find y as a function of a if y(0) = 6, y'(0) = 24, y"(0) = 108. y" + 36y' = 0,

Find y as a function of a if y(0) = 6, y'(0) = 24, y"(0) = 108. y" + 36y' = 0,

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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Find y as a function of if y(0) = 6, y'(0) = 24, "(0) = 108. y(x) y" + 36y' = 0,
Transcribed Image Text:Find y as a function of if y(0) = 6, y'(0) = 24, "(0) = 108. y(x) y" + 36y' = 0,
Expert Solution
Step 1: We have given a differential equation

y′′′+36y′=0

y(0)=6,y′(0)=24,y′′(0)=108.

The characteristic equation is

r3+36r=0r(r2+36)=0r=0,r=±6ir1=0,α±iβ=0±6ir1=0,α=0,β=6

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