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Exam 3 - Spring 2004

# Exam 3 - Spring 2004 - 3 t t t t f in terms of unit step...

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Differential Equations Exam # 3 Spring 2004 Name _______________________ Show all your work neatly and in numerical order on notebook paper. Solutions without correct supporting work will not be accepted. 1. Use the definition of the Laplace transform to find { } 7 + t e L . 2. Find { } ) ( t f L for the following functions: a. t t e t f t 5 cos 2 ) ( 3 3 + - = b. ) 4 ( ) ( 4 3 + + = - t e t t f t δ 3. a. Find + - s s L 3 1 2 1 b. Find - - 2 1 ) 2 ( 7 s s L 4. a. Find - - - s e s L 2 1 4 1 b. Find { } 3 1 t L 5. a. Find { } ) 2 ( 2 - - t U e L t b. Find { } ) 3 ( ) 1 4 ( - + t U t L 6. Write < < = 5 , 7
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Unformatted text preview: , 3 ) ( t t t t f in terms of unit step functions. 7. Use the Laplace transform to solve: 2 ) ( , 6 4 = = + ′ y e y y t 8. Use the Laplace transform to solve: 5 ) ( , 2 ) ( , 3 cos 9 = ′ = = + ′ ′ y y t y y 9. Find the general solution of the system. y x dt dy y x dt dx 3 4 2 + = + = 10. Find the general solution of the system. X X -= ′ 1 1 1 3 1...
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