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function y(t) is a solution of the initial value problem y" + ay' + by = 0,

function y(t) is a solution of the initial value problem y" + ay' + by = 0,

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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Please do #13

 

section 3.5

Exercises 13-21: The function y(t) is a solution of the initial value problem y' + ay' + by = 0, y(to) = Yo, y (to) = y6, where the point to is specified. Determine the constants a, b, Yo, and y,. 13. y(t) = sint – /2 cost, to = 1/4 14. y(t) = 2 sin 2t + cos 2t, to = 1/4 15. y(t) = e-2" cost – e-" sin t, to = 0 16. y(t) = e'-/6 cos 2t – e-/ sin 2t, to = 7/6 17. y(t) = /3 coS nt – sin at, to = 1/2 Cos 18. y(t) = /2 cos(2t – 7/4), to = 0 19. y(t) = 2e' cos(nt – n), to = 1 20. y(t) = e cos(nt – a), to = 0 21. y(t) = 3e-2 cos(t – 1/2), to =0
Transcribed Image Text:Exercises 13-21: The function y(t) is a solution of the initial value problem y' + ay' + by = 0, y(to) = Yo, y (to) = y6, where the point to is specified. Determine the constants a, b, Yo, and y,. 13. y(t) = sint – /2 cost, to = 1/4 14. y(t) = 2 sin 2t + cos 2t, to = 1/4 15. y(t) = e-2" cost – e-" sin t, to = 0 16. y(t) = e'-/6 cos 2t – e-/ sin 2t, to = 7/6 17. y(t) = /3 coS nt – sin at, to = 1/2 Cos 18. y(t) = /2 cos(2t – 7/4), to = 0 19. y(t) = 2e' cos(nt – n), to = 1 20. y(t) = e cos(nt – a), to = 0 21. y(t) = 3e-2 cos(t – 1/2), to =0
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