Exam 2 - Spring 2004

Exam 2 - Spring 2004 - -= y x D y D Dx 8 Solve using the...

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Differential Equations Exam #2 Spring 2004 Name_________________________________ Show all your work neatly and in numerical order on notebook paper. DO NOT WRITE ON THE BACKS OF YOUR PAGES. 1. Given that x x c e c e c y 3 2 2 1 + = - is the complementary function for ) ( 6 x g y y y = - - , write the form of the particular solution for the given values of ) ( x g . Do not solve. a. x x g 4 sin ) ( = b. x xe x g 3 ) ( = 2. Solve: ( 29 0 ' ' ' ' ' 4 = + + y y y 3. Solve: x y y 6 5 - = + 4. a. Find a linear differential operator that annihilates x x x 4 sin 9 13 2 - + . b. Find a linear differential operator that annihilates x e x 5 3 . 5. Use variation of parameters to solve: x e y y y sin 2 3 = + + 6. Solve: 0 8 4 2 2 2 = + + y dx dy x dx y d x 7. Solve the system: ( 29 ( 29 0 2 3 0 2 =
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Unformatted text preview: --= + + y x D y D Dx 8. Solve using the substitution y u ′ = : ( 29 ( 29 2 1 y y y ′ = ′ ′ + 9. A 12-pound weight stretches a spring 2 feet. The weight is released from a point 1 foot below the equilibrium position with an upward velocity of 4 ft/sec. a. Find the equation describing the resulting simple harmonic motion. b. At what time does the weight return to the point 1 foot below equilibrium position? 10. Find the eigenvalues and eigenfunctions for 4 , ) ( , = = = + ′ ′ π λ y y y y ....
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