# 6 10 pts compute when f t 1 f s t a f s 7 2 s 1 3 b f

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______________________________________________________________________ 6. (10 pts.) Compute when f ( t ) 1 { F ( s )}( t ) (a) F ( s ) 7 (2 s 1) 3 (b) F ( s ) 2 s 12 s 2 6 s 13 ______________________________________________________________________ 7. (5 pts.) Circle the letter corresponding to the correct response: If ,then F ( s ) = F ( s ) { t 2 sin( bt )}( s ) (a) (b) 2 s 3 b ( s 2 b 2 ) d ds 2 bs ( s 2 b 2 ) 2 (c) (d) d 2 ds 2 b s 2 b 2 2 bs s 2 ( s 2 b 2 ) 2 (e) None of the above.

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TEST3/MAP2302 Page 4 of 4 ______________________________________________________________________ 8. (15 pts.) Transform the given initial value problem into an algebraic equation in { y } and solve for { y }. Do not take inverse transforms and do not attempt to combine terms over a common denominator. Be very careful. 3 y ( t ) 5 y ( t ) 7 y ( t ) sin(2 t ) ; y (0) 4 , y (0) 6 . ______________________________________________________________________ 9. (10 pts.) The solution to a certain linear ordinary differential equation with coefficient functions that are analytic at x 0 = 0 is of the form y ( x ) n 0 c n x n where the coefficients satisfy the following equations: and c 2 0, c 0 3 c 1 6 c 3 0, c n 2 n ( n 2) c n c n 1 ( n 2)( n 1) for all n 2. Determine the exact numerical value of the coefficients c 0 , c 1 , c 2 , c 3 , and c 4 for the particular solution that satisfies the initial conditions y (0) = 0 and y (0) = 1. c 0 c 1 c 2 c 3 c 4 _________________________________________________________________ Silly 10 Point Bonus: Write the function f ( t ) cos 5 ( bt ) as a linear combination of sine and/or cosines actually appearing in the Laplace transform table provided. Say where your work is, for it won’t fit here.
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