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Unformatted text preview: LaplaceTransformSolutionOfODEs (c) 2006 K.E. Holbert Page 1 of 2 Laplace Transform Solution of Ordinary Differential Equations The Laplace transform converts differential equations in the time domain to algebraic equations in the frequency domain. There are three important steps to the process: (1) transform ODE from the time domain to the frequency domain; (2) manipulate the algebraic equations to form a solution; and (3) inverse transform the solution from the frequency to the time domain. Perhaps, the most common Laplace transform pairs are those appearing in the table below: f ( t ) ( t ) u ( t ) t a e t F ( s ) 1 s 1 a s + 1 2 1 s When applied to differential equations, Laplace transforms automatically account for initial conditions via ) ( ) ( ) ( ) ( ) ( ) ( ) ( 2 2 2 y y s s s dt t y d x s s dt t x d L L = = Y X (1) Inverse Laplace Transform Performing the inverse transform is straightforward when using partial fractions expansion with the...
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This note was uploaded on 02/06/2012 for the course EEE 460 taught by Professor Holbert during the Spring '06 term at ASU.
- Spring '06