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Use the Laplace transform to solve the following initial value problem: y" - 6y - 16y=0 y(0) = 1, y'(0) = 6 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 s²y-s-6sY-16Y = 0 S ²-65-16 Now solve for Y(s) s+a and write the above answer in its partial fraction decomposition, Y(s) = a + Y(s) = 0 + 0 Now by inverting the transform, find y(t) = B 8+6 where a < b

Use the Laplace transform to solve the following initial value problem: y" - 6y - 16y=0 y(0) = 1, y'(0) = 6 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 s²y-s-6sY-16Y = 0 S ²-65-16 Now solve for Y(s) s+a and write the above answer in its partial fraction decomposition, Y(s) = a + Y(s) = 0 + 0 Now by inverting the transform, find y(t) = B 8+6 where a < b

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" - 6y - 16y=0 y(0) = 1, y'(0) = 6 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 s²y-s-6sY-16Y = 0 S ²-65-16 Now solve for Y(s) s+a and write the above answer in its partial fraction decomposition, Y(s) = a + Y(s) = 0 + 0 Now by inverting the transform, find y(t) = B 8+6 where a < b
Transcribed Image Text:Use the Laplace transform to solve the following initial value problem: y" - 6y - 16y=0 y(0) = 1, y'(0) = 6 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 s²y-s-6sY-16Y = 0 S ²-65-16 Now solve for Y(s) s+a and write the above answer in its partial fraction decomposition, Y(s) = a + Y(s) = 0 + 0 Now by inverting the transform, find y(t) = B 8+6 where a < b
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