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(10) d'y dx² 2 dy dx + 2y = sin x HINT: For homogenous solution, substitute y = Aex to find roots of characteristic equations r₁= 1+i and r2=1-i; For particular solution use undetermined coefficients of the form yp-asin(x)+bcos(x). Substitute into original ODE to find a=1/5 and b=2/5; ANSWER: y = ex(Asinx+ Bcosx) + 1/5sin x +2/5cos x

(10) d'y dx² 2 dy dx + 2y = sin x HINT: For homogenous solution, substitute y = Aex to find roots of characteristic equations r₁= 1+i and r2=1-i; For particular solution use undetermined coefficients of the form yp-asin(x)+bcos(x). Substitute into original ODE to find a=1/5 and b=2/5; ANSWER: y = ex(Asinx+ Bcosx) + 1/5sin x +2/5cos x

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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(10) d'y dx² 2 dy dx + 2y = sin x HINT: For homogenous solution, substitute y = Aex to find roots of characteristic equations r₁= 1+i and r2=1-i; For particular solution use undetermined coefficients of the form yp-asin(x)+bcos(x). Substitute into original ODE to find a=1/5 and b=2/5; ANSWER: y = ex(Asinx+ Bcosx) + 1/5sin x +2/5cos x
Transcribed Image Text:(10) d'y dx² 2 dy dx + 2y = sin x HINT: For homogenous solution, substitute y = Aex to find roots of characteristic equations r₁= 1+i and r2=1-i; For particular solution use undetermined coefficients of the form yp-asin(x)+bcos(x). Substitute into original ODE to find a=1/5 and b=2/5; ANSWER: y = ex(Asinx+ Bcosx) + 1/5sin x +2/5cos x
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