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Unformatted text preview: Name : UF ID number : Quiz 3, MAP 2302, Fall11 Show your work! Write your name on every piece of paper you turn in! 1 . Find a general solution of the equation y primeprimeprime- 3 y primeprime + 3 y prime- y = e x 2 . Find the Laplace transform of f ( t ) = t sin 2 t 3 . Find the function whose Laplace transform is F ( s ) = 7 s 2 + 23 s + 30 ( s- 2)( s 2 + 2 s + 5) 4 . Use the method of Laplace transforms to solve the initial value problem: y primeprime + 3 ty prime- 6 y = 1 , y (0) = y prime (0) = 0 Hint: Recall dy dx + p ( x ) y = q ( x ) y ( x ) = 1 ( x ) integraldisplay ( x ) q ( x ) dx, ( x ) = exp parenleftbiggintegraldisplay p ( x ) dx parenrightbigg 5 . Find the Laplace transform of the solution of the initial value problem: y primeprime + 3 y prime + 2 y = e- 3 t u ( t- 2) , y (0) = 2 , y prime (0) =- 3 where u ( t ) is the step function ( u ( t ) = 1 if t 0 and u ( t ) = 0 elsewhere). Extra credit : Find the solution. 6 ( Extra credit ). Consider the initial value problem y primeprime + 2 y prime + 5 y = g ( t ), y (0) = y prime (0) = 0, where g ( t ) = 1 a = const > 0 if 0 < t < a and g ( t ) = 0 elsewhere. Find the solution of this problem in the limit when a 0. Some properties of the Laplace transform F ( s ) = L ( f ) = integraldisplay e- st f ( t ) dt, s > L ( t n ) = n ! s n +1 , n = 0 , 1 , 2 , ..., 0! = 1 , s > L ( e at t n ) = n !...
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This note was uploaded on 12/15/2011 for the course MAP 2302 taught by Professor Tuncer during the Spring '08 term at University of Florida.
- Spring '08