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Use the Laplace transform to solve the given initial value problem. y(t) = 0 1 2 exp(1 t) + 1 1 - exp(-2t) 1 - exp(2t) exp(t + 2) - 1 1- exp(t + 2) 2 exp(t+1) + 1 1 + exp(-2t) 1 + exp(2t) 2 exp(-t-1)-2 2-2 exp(-t-1) exp(-t-1) + 1 2 exp(1-1)-2 2-2 exp(1-t) No solution y' + y = f(t), y(0) = 0, where f(t) = +( ✓ ) U(t- V 0, 0≤t<1 {2, tz1

Use the Laplace transform to solve the given initial value problem. y(t) = 0 1 2 exp(1 t) + 1 1 - exp(-2t) 1 - exp(2t) exp(t + 2) - 1 1- exp(t + 2) 2 exp(t+1) + 1 1 + exp(-2t) 1 + exp(2t) 2 exp(-t-1)-2 2-2 exp(-t-1) exp(-t-1) + 1 2 exp(1-1)-2 2-2 exp(1-t) No solution y' + y = f(t), y(0) = 0, where f(t) = +( ✓ ) U(t- V 0, 0≤t<1 {2, tz1

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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Use the Laplace transform to solve the given initial value problem. y(t) = 0 1 2 exp(1 t) + 1 1 - exp(-2t) 1 - exp(2t) exp(t + 2) - 1 1 - exp(t + 2) 2 exp(t + 1) + 1 1 + exp(-2t) 1 + exp(2t) 2 exp(-t-1)-2 2-2 exp(-t-1) exp(-t-1) + 1 2 exp(1-t) - 2 2-2 exp(1 – t) No solution 0, 0≤t<1 y'+y=f(t), y(0) = 0, where f(t) = {2, t>1 +( ✓ ) U(t- ✓ )
Transcribed Image Text:Use the Laplace transform to solve the given initial value problem. y(t) = 0 1 2 exp(1 t) + 1 1 - exp(-2t) 1 - exp(2t) exp(t + 2) - 1 1 - exp(t + 2) 2 exp(t + 1) + 1 1 + exp(-2t) 1 + exp(2t) 2 exp(-t-1)-2 2-2 exp(-t-1) exp(-t-1) + 1 2 exp(1-t) - 2 2-2 exp(1 – t) No solution 0, 0≤t<1 y'+y=f(t), y(0) = 0, where f(t) = {2, t>1 +( ✓ ) U(t- ✓ )
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