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Find the general solution of each of the differential equations. y" – 4y' + 4y = 0

Find the general solution of each of the differential equations. y" – 4y' + 4y = 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 the general solution of each of the differential equations. y" – 4y' + 4y = 0
Transcribed Image Text:Find the general solution of each of the differential equations. y" – 4y' + 4y = 0
B- Exompes Exauple I.find the goneral solv Hon y. d"-2y' -3y 2ex -10x 1) ST S2 = e Once de'yi bulalım: =sinx, cos* 2) Herhang! bir Flame gerele yot 3) Aerhongi bir Relenme 4) Ae + Bsinx+ Ccosa Aet B sinx genelk yot. (r-3) (r+1) -U 5) Yp - + Ccosx Yp'= Ae + Bcosx -csihx. y= A ex -Bsinx Bunbri denk lemce yerine koyersrak: + Cze %3D (AeX - B sinx -C cosx) -2(Ae*+Bcosx -Csinx) 3 (Aex+B sinx + Ccosx) HAe' +(-B+2C+38)sinx+ (-C -2 B-3C)coSx=2e 1erax -4A=2 A= 2-4B+2C=-10 %3D ー4+2C= 10 ー4C-28=O - -20 ー4C-2.2 =0 I devaur ortode ○ sで-つケー ちこうと dp =Ze 1. *+2 sinx- COSX Gerenal Solution: 2. 3メ4C X- 1e*+ 25inx - cosk. 2. Example:
Transcribed Image Text:B- Exompes Exauple I.find the goneral solv Hon y. d"-2y' -3y 2ex -10x 1) ST S2 = e Once de'yi bulalım: =sinx, cos* 2) Herhang! bir Flame gerele yot 3) Aerhongi bir Relenme 4) Ae + Bsinx+ Ccosa Aet B sinx genelk yot. (r-3) (r+1) -U 5) Yp - + Ccosx Yp'= Ae + Bcosx -csihx. y= A ex -Bsinx Bunbri denk lemce yerine koyersrak: + Cze %3D (AeX - B sinx -C cosx) -2(Ae*+Bcosx -Csinx) 3 (Aex+B sinx + Ccosx) HAe' +(-B+2C+38)sinx+ (-C -2 B-3C)coSx=2e 1erax -4A=2 A= 2-4B+2C=-10 %3D ー4+2C= 10 ー4C-28=O - -20 ー4C-2.2 =0 I devaur ortode ○ sで-つケー ちこうと dp =Ze 1. *+2 sinx- COSX Gerenal Solution: 2. 3メ4C X- 1e*+ 25inx - cosk. 2. Example:
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