3 Which form should you use to determine a particular solution of the following differential equation? y(7) – 4y(0) – 4y(5) + 56y(4) – 156y(3) + 224y" – 176y' + 64y = e* cos(x) – 3e2x + xe -4x (1) yp = (A1x? + A2x)e-4x + Aze2x + A4xe* cos(x) + A5xe* sin(x) (2) yp = A1xex + (A2x + A3)e* + A4e* cos(x)+ Age* cos(x) 4х (3) yp = A1xe* cos(x) + A2xe* sin(x) + A3x°ex + (A4x + A5)e (4) yp = A1x°e* cos(x) + A2x'e* sin(x)+ A3x'e* + (A4x² + A5x)e 4x (5) yp = A1x°e2x + (A2x + A3)e 4x + A4e* cos(x)+ Age* sin(x) (6) yp = A1ex + A2xe* cos(x) + A3xe* sin(x) + (A4x + A5)e-4x
3 Which form should you use to determine a particular solution of the following differential equation? y(7) – 4y(0) – 4y(5) + 56y(4) – 156y(3) + 224y" – 176y' + 64y = e* cos(x) – 3e2x + xe -4x (1) yp = (A1x? + A2x)e-4x + Aze2x + A4xe* cos(x) + A5xe* sin(x) (2) yp = A1xex + (A2x + A3)e* + A4e* cos(x)+ Age* cos(x) 4х (3) yp = A1xe* cos(x) + A2xe* sin(x) + A3x°ex + (A4x + A5)e (4) yp = A1x°e* cos(x) + A2x'e* sin(x)+ A3x'e* + (A4x² + A5x)e 4x (5) yp = A1x°e2x + (A2x + A3)e 4x + A4e* cos(x)+ Age* sin(x) (6) yp = A1ex + A2xe* cos(x) + A3xe* sin(x) + (A4x + A5)e-4x
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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3 Which form should you use to determine a particular solution of the following
Transcribed Image Text:3 Which form should you use to determine a particular solution of the following differential equation?
y(7) – 4y6) – 4y(5) + 56y(4) – 156y(3) + 224y" – 176y + 64y = e* cos(x) – 3e2x + xe4x
(1) yp = (A1x? + A2x)e-4x
+ A3e?x + A4xe* cos(x) + A5xe* sin(x)
(2) yp = A1xex + (A2x + A3)e* + A4e* cos(x)+ Age* cos(x)
4х
(3) yp = A1xe* cos(x) + A2xe* sin(x) + A3x°ex + (A4x + A5)e
(4) yp = A1x°e* cos(x) + A2x'e* sin(x)+ A3x?e* + (A4x? + A;x)e 4x
(5) yp = A1x°e2x + (A2x + A3)e 4x + A4e* cos(x)+ Age* sin(x)
(6) yp = A1ex + A2xe* cos(x) + A3xe* sin(x) + (A4x + A5)e-4x
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