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(b) Use a computer algebra system to find a particular solution of the given equation. Y(t) (-1e¹(-30te*cos(t) + 30te'sin(t) — 10e'cos(t) + 80e'sin(t) + 3 sin(2t) + cc= =

(b) Use a computer algebra system to find a particular solution of the given equation. Y(t) (-1e¹(-30te*cos(t) + 30te'sin(t) — 10e'cos(t) + 80e'sin(t) + 3 sin(2t) + cc= =

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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Consider the following. (A computer algebra system is recommended.) y" - 5y' + 6y = et cos 2t + e²t(3t+ 4)sin t (a) Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. Y(t) = = et(A₁ cos 2t + A₂ sin 2t) + (B₁ + B₂t)et sin t + (C₁ + C₂t)et cos t Y(t) = et (A₁ cos t + A₂ sin t) + (B₁ + B₂t)e²t sin t + (C₁ + C₂t)e²t cos t Y(t) = e(A₁ cos 2t + A₂ sin 2t) + (B₁ + B₂t)e²t sin t + (C₁ + C₂t)e²t cos t Y(t) O y(t) = Y(t) = = e²t (A₁ cos 2t + A2₂ sin 2t) + (B₁ + B₂t)et sin t + (C₁ + С₂t)et cos t e²t (A₁ cos t + A₂ sin t) + (B₁ + B₂t)e²t sin t + (C₁ + С₂t)e²t cos t (b) Use a computer algebra system to find a particular solution of the given equation. 1 20 ¹( −30teʼcos(t) + 30teʼsin(t) — 10e'cos(t) + 80eʼsin(t) + 3 sin(2t) + cos cos (2t)) X
Transcribed Image Text:Consider the following. (A computer algebra system is recommended.) y" - 5y' + 6y = et cos 2t + e²t(3t+ 4)sin t (a) Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. Y(t) = = et(A₁ cos 2t + A₂ sin 2t) + (B₁ + B₂t)et sin t + (C₁ + C₂t)et cos t Y(t) = et (A₁ cos t + A₂ sin t) + (B₁ + B₂t)e²t sin t + (C₁ + C₂t)e²t cos t Y(t) = e(A₁ cos 2t + A₂ sin 2t) + (B₁ + B₂t)e²t sin t + (C₁ + C₂t)e²t cos t Y(t) O y(t) = Y(t) = = e²t (A₁ cos 2t + A2₂ sin 2t) + (B₁ + B₂t)et sin t + (C₁ + С₂t)et cos t e²t (A₁ cos t + A₂ sin t) + (B₁ + B₂t)e²t sin t + (C₁ + С₂t)e²t cos t (b) Use a computer algebra system to find a particular solution of the given equation. 1 20 ¹( −30teʼcos(t) + 30teʼsin(t) — 10e'cos(t) + 80eʼsin(t) + 3 sin(2t) + cos cos (2t)) X
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