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3 Which form should you use to determine a particular solution of the following differential equation? y(7)-4y(@)-4y(6) +56y(4)- 156y(3) + 224y"-176y +64y = e cos(x) – 3e* (Submit the corresponding number without parentheses.) +xe-4x

3 Which form should you use to determine a particular solution of the following differential equation? y(7)-4y(@)-4y(6) +56y(4)- 156y(3) + 224y"-176y +64y = e cos(x) – 3e* (Submit the corresponding number without parentheses.) +xe-4x

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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teristic equation or the 3 Which form should you use to determine a particular solution of the following differetial equation? 4y(6) y(7)-4y6)-4y(5)+56y4)- 156y3) +224y"- x+ xe 176y +64y = e cos(x)-3e -4x (Submit the corresponding number without parentheses.) (1) yp = (A1x + A2x)e 4x+ A3e2x + A4xe* cos(x) + A5xe* sin(x) (2) yp = A1xe+ (A2x + A3)e + A4e* cos(x) + Age* cos(x) (3) yp = A1xe* cos(x) + A2xe* sin(x) + A3x²e²* +(A4x+A5)e 4x (4) yp = A1x?e* cos(x) + A2x²e* sin(x) + A3x²e²x + (A4x² + Agx)e 4x A1x e* cos(x) + A2x e* sin(x) + A3: + (A4x² + A5x)e (5) yp = A1x ex + (A2X + A3)e 4x +A4e* cos(x) + Aze sin(x) (6) yp = Aje²x + A2xe* cos(x) + A3xe* sin(x) + (A4x + A5 e 4x Hint: You may use https:///www.wolframalpha.com/ or a computer program to factorize the charac- teristic equation of the corresponding homogencous differential equation.
Transcribed Image Text:teristic equation or the 3 Which form should you use to determine a particular solution of the following differetial equation? 4y(6) y(7)-4y6)-4y(5)+56y4)- 156y3) +224y"- x+ xe 176y +64y = e cos(x)-3e -4x (Submit the corresponding number without parentheses.) (1) yp = (A1x + A2x)e 4x+ A3e2x + A4xe* cos(x) + A5xe* sin(x) (2) yp = A1xe+ (A2x + A3)e + A4e* cos(x) + Age* cos(x) (3) yp = A1xe* cos(x) + A2xe* sin(x) + A3x²e²* +(A4x+A5)e 4x (4) yp = A1x?e* cos(x) + A2x²e* sin(x) + A3x²e²x + (A4x² + Agx)e 4x A1x e* cos(x) + A2x e* sin(x) + A3: + (A4x² + A5x)e (5) yp = A1x ex + (A2X + A3)e 4x +A4e* cos(x) + Aze sin(x) (6) yp = Aje²x + A2xe* cos(x) + A3xe* sin(x) + (A4x + A5 e 4x Hint: You may use https:///www.wolframalpha.com/ or a computer program to factorize the charac- teristic equation of the corresponding homogencous differential equation.
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