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Unformatted text preview: L [ f ] = [ ] ) 1 ( 1 ) 1 ( 1 ) 1 ( 1 1 1 ) ( 1 1 2 1 2 1 2 2 2 s s s st s st s st s e s e s e e e s dt e e dt e t f e+ ====âˆ« âˆ« . 5. (6 marks) Use Laplace transformation to solve the differential equation t f ( t ) MATH3705 Solution to Test 1 Summer 2006 2 y" + y = e t , y (0) = 0, y' (0) = 1. Solution . Let Y ( s ) = L [ y ]. Take the Laplace transformation on both sides: s 2 Y1 + Y = 1 / ( s1). ( s 2 + 1) Y = s / ( s1). Y = s / [( s1)( s 2 + 1)] = (1 / 2)(1 / ( s1) s / ( s 2 + 1) + 1 / ( s 2 + 1)). Take the inverse Laplace transformation, using the result in Question 1 and 2, y = (1 / 2)( e tcos t + sin t )....
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 Winter '08
 JaberAbdualrahman
 Fractions, Laplace, Rational function, 2k, 0 2k

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