1. Use the method of undetermined coefficients to find a particular solution to the following differential equation. y" -/ +9y = 3 sin 3t r?-r+9=0 -4BSn3t-3ACOS 3E - 2BSN2E19B0626

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1. Use the method of undetermined coefficients to find a particular solution to the following differential equation.
y" - y + 9y = 3 sin 3t
r?-r+9=0
-4BSn3t -3ACOS 3E - 2BSn2t +9BC052E
(9BCOSZE -BACOS3t)+64Bsn3t-2BSinizE
21)
2.
O yo)=G,ecos C.e sin
@ Yp = ASn 3t + BOS3E
O yp' = 3A CCS 3t - 28sin 3t
yp" - 9ASn3t -4BSN3
-9ASin 3t -4BSın3t)-(3ACOS3E-2BSm8t)+9(A Sin 3++ BCOS36)- 35in2t
%3D
2. Given that yi(t) = e2t is a solution to y"-y/+ 9y = 1le", find a particular solution to
%3D
y" – / + 9y = 6 sin 3t + 33et
%3D
hint: use your answer from problem 1 and the superposition principle.
Transcribed Image Text:1. Use the method of undetermined coefficients to find a particular solution to the following differential equation. y" - y + 9y = 3 sin 3t r?-r+9=0 -4BSn3t -3ACOS 3E - 2BSn2t +9BC052E (9BCOSZE -BACOS3t)+64Bsn3t-2BSinizE 21) 2. O yo)=G,ecos C.e sin @ Yp = ASn 3t + BOS3E O yp' = 3A CCS 3t - 28sin 3t yp" - 9ASn3t -4BSN3 -9ASin 3t -4BSın3t)-(3ACOS3E-2BSm8t)+9(A Sin 3++ BCOS36)- 35in2t %3D 2. Given that yi(t) = e2t is a solution to y"-y/+ 9y = 1le", find a particular solution to %3D y" – / + 9y = 6 sin 3t + 33et %3D hint: use your answer from problem 1 and the superposition principle.
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