In Problems 4-7, use the Laplace transform to solve the IVP. You can use the following dictio- nary: C{eat}= L{cos(wt)} L{sin(wt)} = = 1 s-a S 8² +w²¹ W s² + w²¹ n! gn+1 = 0, 1, 2,..., C{"}= C{8(t-T)}=e-T, e-T L{H(t-T)}= 8 and the following list of rules (where F(s) = L{f(t)}): C{f'(t)} = sF(s)-f(0), L{f"(t)} = s²F(s) - sf (0) - f'(0). F(8) 8 c{ ["s(u) du}=\ C{tf(t)} = == -F(s), ds L{f(t-T)H(t-T)} = e-TF(s), L{c f(t)} = F(s-c). 4. y' + 2y = et, y(0) = 0. 5. yy=1-H(t-2), y(0) = 1, y'(0) = 0. 6. y" - 2y + y = 1²8(t-3), y(0) = 0, y' (0) = 0. 7. yy=(t-3)H(t-3). y(0) = 1.
In Problems 4-7, use the Laplace transform to solve the IVP. You can use the following dictio- nary: C{eat}= L{cos(wt)} L{sin(wt)} = = 1 s-a S 8² +w²¹ W s² + w²¹ n! gn+1 = 0, 1, 2,..., C{"}= C{8(t-T)}=e-T, e-T L{H(t-T)}= 8 and the following list of rules (where F(s) = L{f(t)}): C{f'(t)} = sF(s)-f(0), L{f"(t)} = s²F(s) - sf (0) - f'(0). F(8) 8 c{ ["s(u) du}=\ C{tf(t)} = == -F(s), ds L{f(t-T)H(t-T)} = e-TF(s), L{c f(t)} = F(s-c). 4. y' + 2y = et, y(0) = 0. 5. yy=1-H(t-2), y(0) = 1, y'(0) = 0. 6. y" - 2y + y = 1²8(t-3), y(0) = 0, y' (0) = 0. 7. yy=(t-3)H(t-3). y(0) = 1.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.5: Derivatives Of Logarithmic Functions
Problem 47E
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Transcribed Image Text:In Problems 4-7, use the Laplace transform to solve the IVP. You can use the following dictio-
nary:
C{eat}=
=
L{cos(wt)}
L{sin(wt)} =
=
1
s-a
S
8² +w²¹
W
s² + w²¹
H
n!
gn+1 = 0, 1, 2,...,
C{"}=
C{8(t-T)} = e-T,
e-^T
L{H(t-T)}=
8
and the following list of rules (where F(s) = L{f(t)}):
C{f'(t)} = sF(s)-f(0),
L{f"(t)} = s²F(s) - sf (0) - f'(0).
F(s)
8
c{ ["s(u) du}=\
C{tf(t)} = F(s),
ds
L{f(t-T)H(t-T)} = e-TF(s),
L{c f(t)} = F(s-c).
4. y' + 2y = et, y(0) = 0.
5. yy=1-H(t-2), y(0) = 1, y'(0) = 0.
6. y" - 2y + y = 1²(t-3), y(0) = 0, y'(0) = 0.
7. yy=(t-3)H(t-3). y(0) = 1.
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