2t -4 0st<2 D2-1)y= t22 y(0)=0, y'(O)=1 Find L{y}

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2t-4 0st<2
D²-1)y=
2
t22
y(0)=0, y'(0)=1
Find L{y}
L (1) = F
4
2e 2s
2e-2s
s2 (s² –1)
s(s? –1)
s² (s² –1)
s(s²–1)
°L(w) = + -) -1)(1)
2
4
2e-2s
s2-1
s2 (s2 -1)
s(s2-1)
s2 (s2 -1)
2e 2s
s(s²-1)
L (y) = 1 +
s2
4
2e-2s
2e-2s
-
s2
L (y)
4
s2 (s² –1)
(s²-1)
2e 2s
6e 2s
s² (s² -1)
s(s²-1)
S
(1-2) +
Transcribed Image Text:2t-4 0st<2 D²-1)y= 2 t22 y(0)=0, y'(0)=1 Find L{y} L (1) = F 4 2e 2s 2e-2s s2 (s² –1) s(s? –1) s² (s² –1) s(s²–1) °L(w) = + -) -1)(1) 2 4 2e-2s s2-1 s2 (s2 -1) s(s2-1) s2 (s2 -1) 2e 2s s(s²-1) L (y) = 1 + s2 4 2e-2s 2e-2s - s2 L (y) 4 s2 (s² –1) (s²-1) 2e 2s 6e 2s s² (s² -1) s(s²-1) S (1-2) +
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