# m238sp06t4z - 3-4 e-6 s s 2 3 b 2 s s 2 6 s 25 4 Use the...

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Mathematics 238 test four Friday, June 9, 2006 1 . Simplify each of the following: ( a ) Z 0 ± t 3 e - 5 t ² e - st dt ( b ) u 2 ( t - 4) ( c ) the convolution e t * e - t 2 . Given the function f ( t ) = 6 if t < 3 9 - t if 3 t < 5 4 if t 5 rewrite the function in terms of unit functions u c ( t ) calculate the Laplace transform of the function 3 . Find the function which corresponds to each Laplace transform: ( a ) 4 s 3 - 4 ( s + 2)
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Unformatted text preview: 3-4 e-6 s ( s + 2) 3 ( b ) 2 s s 2 + 6 s + 25 4 . Use the Laplace transform to solve the initial value problem y + y = (2 t + 1) e-t and y (0) = 1 5 . Use the Laplace transform to solve the initial value problem y 00 + y = 1-u π ( t ) and y (0) = 0 and y (0) = 0 and sketch a graph of the solution....
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