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Determine the solution of the following differential equations. a) y"- 6y'+ 9y = 0. b) 4y"- 12y'+ 9y= 0, y(0) = 2 and y'(0)= - 1. 1 c)_4y"+ 4y'+ y= 0, y(0)=2_and_y'(1)= e ¹².

Determine the solution of the following differential equations. a) y"- 6y'+ 9y = 0. b) 4y"- 12y'+ 9y= 0, y(0) = 2 and y'(0)= - 1. 1 c)_4y"+ 4y'+ y= 0, y(0)=2_and_y'(1)= e ¹².

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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Homegeneous Equation. Please help me to solve this exercise
HOMOGENEOUS EQUATION Determine the solution of the following differential equations. a) y"- 6y'+ 9y = 0. b) 4y"- 12y'+ 9y = 0, y(0) = 2 and y'(0)= - 1. c)_4y"+ 4y'+ y= 0, y(0) = 2_and_y'(1)= e ¹². d) y"+ 16y= 0. e) y"- 8y'+ 17y= 0, y(0)= - 4 and y'(0)= - 1. f) y"- 4y'+ 9y= 0, y(0) = 0 and y'(0) = - 8. a) y(x)= (A+ Bx)e³x. y(x)= 2(1-2x)e²¹. y(x) = (4x + 2)e ²*. Answers: y(x)= Acos(4x) + B sin(4x). y(x)= e(- 4 cos x + 15 sin x). 8 y(x) = - -e²* sin (√5x). √5 14 ZY-2022-SMQ10203 b) c) d) e) f)
Transcribed Image Text:HOMOGENEOUS EQUATION Determine the solution of the following differential equations. a) y"- 6y'+ 9y = 0. b) 4y"- 12y'+ 9y = 0, y(0) = 2 and y'(0)= - 1. c)_4y"+ 4y'+ y= 0, y(0) = 2_and_y'(1)= e ¹². d) y"+ 16y= 0. e) y"- 8y'+ 17y= 0, y(0)= - 4 and y'(0)= - 1. f) y"- 4y'+ 9y= 0, y(0) = 0 and y'(0) = - 8. a) y(x)= (A+ Bx)e³x. y(x)= 2(1-2x)e²¹. y(x) = (4x + 2)e ²*. Answers: y(x)= Acos(4x) + B sin(4x). y(x)= e(- 4 cos x + 15 sin x). 8 y(x) = - -e²* sin (√5x). √5 14 ZY-2022-SMQ10203 b) c) d) e) f)
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