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Given the following differential equation: (D² – 4) y = e-3" sin e | Using the method of variation of parameters, which of the following equations result after the proposed particular solution is substituted to the given differential equation?

Given the following differential equation: (D² – 4) y = e-3" sin e | Using the method of variation of parameters, which of the following equations result after the proposed particular solution is substituted to the given differential equation?

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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Given the following differential equation: (D² – 4) y = e-3¤ sin e - %3D | Using the method of variation of parameters, which of the following equations result after the proposed particular solution is substituted to the given differential equation? O A' (x) cos 2x + B' (x) sin 2x = 0 -3x — 2A (х) sin 2x + 2 B (х) cos 2a — е sin e-* ОА (х) сos 2х + B' (х) sin 2x 2A (2) sin 2a - 2B (х) соs 2 х — е' -3x sin e-* ОА (г) е2 + В (х)е 20 -2x = 0 2A' (x) e2a -2x -3x -2x O A' (x) e2a + B' (x) e = 0 2A (х) е2^ + 2B (х) е -2x = e -3x sin e-
Transcribed Image Text:Given the following differential equation: (D² – 4) y = e-3¤ sin e - %3D | Using the method of variation of parameters, which of the following equations result after the proposed particular solution is substituted to the given differential equation? O A' (x) cos 2x + B' (x) sin 2x = 0 -3x — 2A (х) sin 2x + 2 B (х) cos 2a — е sin e-* ОА (х) сos 2х + B' (х) sin 2x 2A (2) sin 2a - 2B (х) соs 2 х — е' -3x sin e-* ОА (г) е2 + В (х)е 20 -2x = 0 2A' (x) e2a -2x -3x -2x O A' (x) e2a + B' (x) e = 0 2A (х) е2^ + 2B (х) е -2x = e -3x sin e-
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