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Unformatted text preview: y ( t ) to (1) is given by (5) y ( t ) = ( y I ( t ) if 0 t < a, y II ( t ) if t a. On the other hand, the application of the Laplace transform to the initial value problem (1) has the advantage of solving the problem in Date : February 22, 2011. 1 2 KIAM HEONG KWA a more direct manner. Let Y ( s ) = L y ( s ). Then taking the Laplace transform of (1) yields ( s 2 + s + ) Y ( s )( s + ) yy = eas s , from which it follows that (6) Y ( s ) = ( s + ) y + y s 2 + s + + eas s ( s 2 + s + ) . The solution y ( t ) to (1) is then obtained by inverting the transform: (7) y ( t ) = L1 [ Y ( s )]( t ) = L1 ( s + ) y + y s 2 + s + + eas s ( s 2 + s + ) ( t ) ....
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 Winter '11
 Kwa
 Differential Equations, Equations

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