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c. write the above answer in its partial fraction decomposition, Y(s) = sq + Y(s) = + d. Now, by inverting the transform, find y(t) = . B (s+a)²

c. write the above answer in its partial fraction decomposition, Y(s) = sq + Y(s) = + d. Now, by inverting the transform, find y(t) = . B (s+a)²

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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c and d

Use the Laplace transform to solve the following initial value problem: y" - 6y +9y=0 y(0) = 5, y/(0) = 2 a. 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 x(s2²-6s+9) b. Solve for Y(s) -6s+ 9)-5s-2 +30 = 0 = 55 - 28 (s-3)² c. write the above answer in its partial fraction decomposition, Y(s) = = Y(s) = + d. Now, by inverting the transform, find y(t) = . A B + s+a (s+a)²
Transcribed Image Text:Use the Laplace transform to solve the following initial value problem: y" - 6y +9y=0 y(0) = 5, y/(0) = 2 a. 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 x(s2²-6s+9) b. Solve for Y(s) -6s+ 9)-5s-2 +30 = 0 = 55 - 28 (s-3)² c. write the above answer in its partial fraction decomposition, Y(s) = = Y(s) = + d. Now, by inverting the transform, find y(t) = . A B + s+a (s+a)²
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