In Exercises 15-24, (a) compute the Laplace transform of both sides of the equation; (b) substitute the initial conditions and solve for the Laplace transform of the solution; (c) find a function whose Laplace transform is the same as the solution; and (d) check that you have found the solution of the initial-value problem.
In Exercises 15-24, (a) compute the Laplace transform of both sides of the equation; (b) substitute the initial conditions and solve for the Laplace transform of the solution; (c) find a function whose Laplace transform is the same as the solution; and (d) check that you have found the solution of the initial-value problem.
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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Transcribed Image Text:In Exercises 15-24,
(a) compute the Laplace transform of both sides of the equation;
(b) substitute the initial conditions and solve for the Laplace transform of the solution;
(c) find a function whose Laplace transform is the same as the solution; and
(d) check that you have found the solution of the initial-value problem.
dy
15. =-y+e-2t,
dt
dy
17. +7y= 1, y(0) = 3
dt
y(0) = 2
dy
19. +9y2, y(0) = -2
dt
dy
16. + 5y = e, y (0) = 2
dt
dy
18. + 4y = 6, y(0) = 0
dt
dy
20. =-y+2, y(0) = 4
dt
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