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Find a particular solution to the differential equation using the Method of Undetermined Coefficients.  y''-y'+9y= 3sin3t *My question is how does the answer end up being cos3t? See picture.

Find a particular solution to the differential equation using the Method of Undetermined Coefficients.  y''-y'+9y= 3sin3t *My question is how does the answer end up being cos3t? See picture.

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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Find a particular solution to the differential equation using the Method of Undetermined Coefficients. 
y''-y'+9y= 3sin3t *My question is how does the answer end up being cos3t? See picture.
y"-y' +9y=3sin 3t y, (t) = Acos 3t+ B sin 3t р a f (t) = -3 Asin 3t+3B cos 3t р Yp (t) = -9 Acos 3t -9B sin 3t р (-9 A cos 3t -9 B sin 3t) -(-3 Asin 3t+ 3B cos3t) +9(Acos 3t+ B sin 3t) = 3sin 3t A=1, B=0 -3B cos 3t+3 Asin 3t = 3sin 3t y, (t) = cos 3t Yp р
Transcribed Image Text:y"-y' +9y=3sin 3t y, (t) = Acos 3t+ B sin 3t р a f (t) = -3 Asin 3t+3B cos 3t р Yp (t) = -9 Acos 3t -9B sin 3t р (-9 A cos 3t -9 B sin 3t) -(-3 Asin 3t+ 3B cos3t) +9(Acos 3t+ B sin 3t) = 3sin 3t A=1, B=0 -3B cos 3t+3 Asin 3t = 3sin 3t y, (t) = cos 3t Yp р
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