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5. y"-y=1-H(t-2), y(0) = 1, y'(0) = 0. +28(+ 2) (0) 101206 0 (0)7

5. y"-y=1-H(t-2), y(0) = 1, y'(0) = 0. +28(+ 2) (0) 101206 0 (0)7

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: L{eat} = L{cos(wt)} = L{sin(wt)} = 1 8-a 8 82 +w21 لیا 8² +6² n! gn+1, n = 0, 1, 2,..., L{t"} = L{8(t-T)} = e-ST e-st L{H(t - T)} 8 and the following list of rules (where F(s) = L{f(t)}): L{f'(t)} = sF(s) - f(0), L{f"(t)} = s²F(s) - sf (0) - f'(0), c { [ * f(u) du} = F(s), d - F(s), ds L{tf(t)} = L{f(t-T)H(t-T)} = e-TF(s), L{ect f(t)} = F(s - c). 4. y' + 2yet, y(0) = 0. 5. y" -y 1-H(t− 2), y(0) = 1, y'(0) = 0. 6. y" - 2y + y = t²8(t− 3), y(0) = 0, y'(0) = 0. y=(t-3)H(t-3), y(0) = 1. 7. y'
Transcribed Image Text:In Problems 4-7, use the Laplace transform to solve the IVP. You can use the following dictio- nary: L{eat} = L{cos(wt)} = L{sin(wt)} = 1 8-a 8 82 +w21 لیا 8² +6² n! gn+1, n = 0, 1, 2,..., L{t"} = L{8(t-T)} = e-ST e-st L{H(t - T)} 8 and the following list of rules (where F(s) = L{f(t)}): L{f'(t)} = sF(s) - f(0), L{f"(t)} = s²F(s) - sf (0) - f'(0), c { [ * f(u) du} = F(s), d - F(s), ds L{tf(t)} = L{f(t-T)H(t-T)} = e-TF(s), L{ect f(t)} = F(s - c). 4. y' + 2yet, y(0) = 0. 5. y" -y 1-H(t− 2), y(0) = 1, y'(0) = 0. 6. y" - 2y + y = t²8(t− 3), y(0) = 0, y'(0) = 0. y=(t-3)H(t-3), y(0) = 1. 7. y'
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