Consider the initial value problem y" - y'=e¹ cost, y(0) = 0, y'(0) = 0 (a) The Laplace Trabsform of y(t) is given by O A OB. OC. O D. L{y} = − L{y} = OB. L{y} = L{y} = 1 1 s²+25+2 (s+ 1)² +1 OE. None of the above answers is cotrrect -- 3 s 1 1 s(s²-4s+5) s((S-2)² +1) (b) The decomposed Laplace Transformed of y(t) is given by OA 41 1 (S-2)² +1 1 s(s² +28+2) 1 1 s(s²-2s+2) s((S-1)² +1) +5 OD. 41 OC. 11 1 1 -3--2- S = -- +5 3 s S-2 (S-2)² +1 S-2 (S-2)² +1 +4- 1 s((s+ 1)² + 1) S-1 (S-1)² +1 +6 S-1 1 + 2 s 2 (S-1)²+1 2 (S-1)² +1 +4 1 1 (S-1)² +1 1 (S-1)² +1 (c) The solution to the IVP is OA. y(t) = -3-2e²¹ cost+ 6e²¹ sint ,21
Consider the initial value problem y" - y'=e¹ cost, y(0) = 0, y'(0) = 0 (a) The Laplace Trabsform of y(t) is given by O A OB. OC. O D. L{y} = − L{y} = OB. L{y} = L{y} = 1 1 s²+25+2 (s+ 1)² +1 OE. None of the above answers is cotrrect -- 3 s 1 1 s(s²-4s+5) s((S-2)² +1) (b) The decomposed Laplace Transformed of y(t) is given by OA 41 1 (S-2)² +1 1 s(s² +28+2) 1 1 s(s²-2s+2) s((S-1)² +1) +5 OD. 41 OC. 11 1 1 -3--2- S = -- +5 3 s S-2 (S-2)² +1 S-2 (S-2)² +1 +4- 1 s((s+ 1)² + 1) S-1 (S-1)² +1 +6 S-1 1 + 2 s 2 (S-1)²+1 2 (S-1)² +1 +4 1 1 (S-1)² +1 1 (S-1)² +1 (c) The solution to the IVP is OA. y(t) = -3-2e²¹ cost+ 6e²¹ sint ,21
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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8 please show written work part A and B
Transcribed Image Text:Consider the initial value problem
y" - y'=e¹ cost, y(0) = 0, y'(0) = 0
(a) The Laplace Trabsform of y(t) is given by
O A
OB.
OC.
O D.
L{y} = −
L{y}=
OB.
L{y} =
L{y} =
1
1
s²+25+2 (s+1)2² +1
OE. None of the above answers is cotrrect
1
s(s² +28+2)
1
1
s(s²-4s+5) s((S-2)² +1)
(b) The decomposed Laplace Transformed of y(t) is given by
OA 41
1
(S-2)² +1
--+5
3 s
OC. 11
2 s
1
1
s(s²-2s+2) s((s-1)² +1)
OD. 41
1
-3--2-
S
S-2
(S-2)² +1
--+5
3 s
+4
S-2
(S-2)² +1
1
s((s+ 1)² +1)
S-1
(S-1)² +1
+6
1 S-1
1
+
2 (S-1)² +1 2 (S-1)² +1
1
(S-1)² +1
1
+4-
1
(S-1)² +1
(c) The solution to the IVP is
OA. y(t) = -3-2e²¹ cost+6e²¹ sint
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