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Use the Laplace transform to solve the following initial value problem: y" + 2y' = 0 y(0) = 8, y'(0) = 3 %3D First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) = B 8+6 and write the above answer in its partial fraction decomposition, Y(s) A + where a < b sta Y(s) = Now by inverting the transform, find y(t)

Use the Laplace transform to solve the following initial value problem: y" + 2y' = 0 y(0) = 8, y'(0) = 3 %3D First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) = B 8+6 and write the above answer in its partial fraction decomposition, Y(s) A + where a < b sta Y(s) = Now by inverting the transform, find y(t)

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 following initial value problem: y" + 2y' = 0 y(0) = 8, y'(0) = 3 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) B where a < b s+b and write the above answer in its partial fraction decomposition, Y(s) A sta Y(s) = Now by inverting the transform, find y(t)
Transcribed Image Text:: Use the Laplace transform to solve the following initial value problem: y" + 2y' = 0 y(0) = 8, y'(0) = 3 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) B where a < b s+b and write the above answer in its partial fraction decomposition, Y(s) A sta Y(s) = Now by inverting the transform, find y(t)
yl6)= 3 Lig"3= s°L -s(qw) = yl6) Use Toble =s 3s - 7 3. 85L- 24 L= 24 it s?+85 24 5?+85 %3D S+8 Alesse o+8) →8A=24 → A=3 %3D 24 = B(-8 +o) → -8B =24 →B = -3 %3D %3D 4= 3- 3e-80
Transcribed Image Text:yl6)= 3 Lig"3= s°L -s(qw) = yl6) Use Toble =s 3s - 7 3. 85L- 24 L= 24 it s?+85 24 5?+85 %3D S+8 Alesse o+8) →8A=24 → A=3 %3D 24 = B(-8 +o) → -8B =24 →B = -3 %3D %3D 4= 3- 3e-80
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