Consider 1 y"(t) + 2y(t) + 2y(t) = 1², y(0) = y(0) = 0 2 (a) The complementary function ye

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
C and D
(c) A particular solution y(t) of the DE is:
O A.
OB.
O C.
O D.
OB.
Yp (t) =
O C.
-t+
t
Yp (t) = 1²-1² 2
O E. None of the answers is correct
O D.
Yp(t)=21²-²2
-t
Yp(t)= t² et cost -t²e-¹ sint
(d) The solution of the IVP is:
O A.
-t
e
1
y(t) =t² et cost-t² e ¹ sint+
e-¹ sint+=e¹c
2
y(t) = 2t² - t² e
t
y(t) =t²-1² ²
e +
2
²₁ 1
+-
2
y(t) = 2
OE. None of the answers is correct
1
-t+=+e
2
-t
sin t
-t
е cost+
sint
Transcribed Image Text:(c) A particular solution y(t) of the DE is: O A. OB. O C. O D. OB. Yp (t) = O C. -t+ t Yp (t) = 1²-1² 2 O E. None of the answers is correct O D. Yp(t)=21²-²2 -t Yp(t)= t² et cost -t²e-¹ sint (d) The solution of the IVP is: O A. -t e 1 y(t) =t² et cost-t² e ¹ sint+ e-¹ sint+=e¹c 2 y(t) = 2t² - t² e t y(t) =t²-1² ² e + 2 ²₁ 1 +- 2 y(t) = 2 OE. None of the answers is correct 1 -t+=+e 2 -t sin t -t е cost+ sint
Consider the IVP:
1
y"(t) + 2y(t) + 2y(t) = (², y(0) = y(0) = 0
(a) The complementary function ye
Transcribed Image Text:Consider the IVP: 1 y"(t) + 2y(t) + 2y(t) = (², y(0) = y(0) = 0 (a) The complementary function ye
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