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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.

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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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.
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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