Assignment #6 - Stephanie Campbell due at 11:55pm EST...

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Stephanie Campbell Assignment 6 MATH263, Fall 2010 due 11/20/2010 at 11:55pm EST. You may attempt any problem an unlimited number of times. 1. (1 pt) Find the Laplace Transform of the following func- tions: f ( t ) = 6 e - 4 t + 7 t 2 + 2 t + 3 F ( s ) = f ( t ) = 6 e 4 t sin ( 7 t )+ 2 t 3 + 3 e t F ( s ) = f ( t ) = 6 te - 4 t sin ( 7 t ) F ( s ) = Note that there is a table of Laplace transforms in Appendix C, page 1271 thru 1273 of the book. 2. (1 pt) Find the Laplace Transform of the following expres- sions: d 2 y dt 2 + 3 dy dt + 7 y given that y ( 0 ) = 7 and dy dt ( 0 ) = 8. 7 d 2 y dt 2 - dy dt + 5 y given that y ( 0 ) = - 3 and dy dt ( 0 ) = 7. 5 d 2 y dt 2 - 13 dy dt - 8 y given that y ( 0 ) = - 7 and dy dt ( 0 ) = 3. Please note that your answers should be functions of Y and s , Y being the Laplace transform of y . Do not use the notation Y ( s ) to write the Laplace transform of y . Webwork will interpret Y ( s ) as Y * ( s ) . 3. (1 pt) Find the Inverse Laplace Transform of the following functions: F ( s ) = s + 6 s 2 - 9 s + 20 f ( t ) = F ( s ) = 4 s + 5 s 2 + s + 6 f ( t ) = F ( s ) = s + 6 s 2 - 10 s + 25 f ( t ) = 4. (1 pt) Consider the initial value problem d 2 y dt 2 + 10 dy dt + 25 y = - 2 e - 5 t - e 6 t , y ( 0 ) = - 8 , dy dt ( 0 ) = -
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