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21 y" + 2y = 4. 22 3y" – y' = 2(4 – t). 23 y" + 4y = 4 cos(2t). 24 9y" + 4y = -48 sin(2t/3). 25 y" – 2y' + y =t-3e'. 26 4y" + 4y' +y = -8(t-2 +t-4)e-t/2.

21 y" + 2y = 4. 22 3y" – y' = 2(4 – t). 23 y" + 4y = 4 cos(2t). 24 9y" + 4y = -48 sin(2t/3). 25 y" – 2y' + y =t-3e'. 26 4y" + 4y' +y = -8(t-2 +t-4)e-t/2.

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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In 21-26, us the method of variation of parameters to find a particular solution the of the given DE. Work from first principles without applying formula (21) directly.
Integrating to find uj and uz and then replacing these functions in (4.19), we obtain the PS yı(t)f(t) y2 (t)f(t) yp(t) = -y1(t) W dt + y2(t) | dt. (4.21) [y1, Y2](t) W[y1, 92](t)
Transcribed Image Text:Integrating to find uj and uz and then replacing these functions in (4.19), we obtain the PS yı(t)f(t) y2 (t)f(t) yp(t) = -y1(t) W dt + y2(t) | dt. (4.21) [y1, Y2](t) W[y1, 92](t)
21 y" + 2y = 4. 22 3y" – y' = 2(4 – t). 23 y" + 4y = 4 cos(2t). 24 9y" + 4y = -48 sin(2t/3). 25 y" – 2y' + y =t-3e'. 26 4y" + 4y' +y = -8(t-2 +t-4)e-t/2.
Transcribed Image Text:21 y" + 2y = 4. 22 3y" – y' = 2(4 – t). 23 y" + 4y = 4 cos(2t). 24 9y" + 4y = -48 sin(2t/3). 25 y" – 2y' + y =t-3e'. 26 4y" + 4y' +y = -8(t-2 +t-4)e-t/2.
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