DEFINITION The Laplace Transform Given a function f(t) defined for all t0, the Laplace transform of...
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DEFINITION The Laplace Transform Given a function f(t) defined for all t≥0, the Laplace transform of f is the function F defined as follows: F(s) = £{f(1)} = √e" f(1) dt for all values of s for which the improper integral converges. Recall that an improper integral over an infinite interval is defined as a limit of integrals over bounded intervals; that is, fg(t) g(1) dt = lim b→∞o, (1) g(t) dt. (2) 3 Use Laplace transforms to solve the initial value problem. y"+x+4y=0 x"+x+4y=0 x(0) = 1, y(0) = 0 x' (0) = 0, y' (0) = 1 DEFINITION The Laplace Transform Given a function f(t) defined for all t≥0, the Laplace transform of f is the function F defined as follows: F(s) = £{f(1)} = √e" f(1) dt for all values of s for which the improper integral converges. Recall that an improper integral over an infinite interval is defined as a limit of integrals over bounded intervals; that is, fg(t) g(1) dt = lim b→∞o, (1) g(t) dt. (2) 3 Use Laplace transforms to solve the initial value problem. y"+x+4y=0 x"+x+4y=0 x(0) = 1, y(0) = 0 x' (0) = 0, y' (0) = 1
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SOLUTION STEP BY STEP To solve the given initial value problem using Laplace transforms we need to take the Laplace transform of the given differentia... View the full answer
Related Book For
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
Posted Date:
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