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Exercise. Find the result of the operations indicated in each of the following problems using formulas (F-01) to (F-05). 5. (D³ – 3D² – 4)(e2x sin 2x)

Exercise. Find the result of the operations indicated in each of the following problems using formulas (F-01) to (F-05). 5. (D³ – 3D² – 4)(e2x sin 2x)

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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Exercise. Find the result of the operations indicated in each of the following problems using formulas (F-01) to (F-05). 5. (D3 — 3D2 — 4)(е2x sin 2x) 6. (хD — 2)(xD + 1)e-2x
Transcribed Image Text:Exercise. Find the result of the operations indicated in each of the following problems using formulas (F-01) to (F-05). 5. (D3 — 3D2 — 4)(е2x sin 2x) 6. (хD — 2)(xD + 1)e-2x
The following formulas for operators may be proven by mathematical induction: F-01. D"eаx 3 а"еах F-02. Ф(D)eax %3D Ф(а)еах F-03. D"(eax)n %3 еаx (D + a)"и = F-04. Ф(D)(eaxи) — е ах Ф(D + a)и F-05. (D — a)"(е ах и) %—D еах D"и
Transcribed Image Text:The following formulas for operators may be proven by mathematical induction: F-01. D"eаx 3 а"еах F-02. Ф(D)eax %3D Ф(а)еах F-03. D"(eax)n %3 еаx (D + a)"и = F-04. Ф(D)(eaxи) — е ах Ф(D + a)и F-05. (D — a)"(е ах и) %—D еах D"и
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