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Determine the particular solution of the ODE below. y" +2y+y=t+e¯t, y (0) = 1, y′ (0) = − 1 a) y (t) = 6e-t + 2e-t + 5e-t + t b) y (t) = -3et+3te-t + t² et + t c) y (t) = 3e¯t + tet+t²e+t-2 d) y (t) = -3et+3te-t +9t² et + 2t - 1

Determine the particular solution of the ODE below. y" +2y+y=t+e¯t, y (0) = 1, y′ (0) = − 1 a) y (t) = 6e-t + 2e-t + 5e-t + t b) y (t) = -3et+3te-t + t² et + t c) y (t) = 3e¯t + tet+t²e+t-2 d) y (t) = -3et+3te-t +9t² et + 2t - 1

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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Question 2 Determine the particular solution of the ODE below. y" + 2y +y=t+et, y (0) = 1, y' (0) = −1 -t a) y (t) = 6e¯t + 2e¯t + 5e¯ª + t b) y (t) = -3et+3te-t + t² et + t c) y (t) = 3e-t + tet+t²e+t-2 d) y(t) = -3e-t +3te-t +9t²e-t +2t - 1 O a b C d
Transcribed Image Text:Question 2 Determine the particular solution of the ODE below. y" + 2y +y=t+et, y (0) = 1, y' (0) = −1 -t a) y (t) = 6e¯t + 2e¯t + 5e¯ª + t b) y (t) = -3et+3te-t + t² et + t c) y (t) = 3e-t + tet+t²e+t-2 d) y(t) = -3e-t +3te-t +9t²e-t +2t - 1 O a b C d
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