23F09-FEReview - Math 3323 Old Final Exam for Review Fall...

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Math 3323 - Old Final Exam for Review Fall 2009 1. (30 points) Solve the following three first order initial value problems. One is linear, one is separable, and one is exact. In each problem, solve for y as an explicit function of t. 2 5 1 (a) (2 12 ), (0) 7 dy y t t y dt 2 2 (b) (2 sec ) ( 2 ) 0, ( ) 10 ty t dt t y dy y 10 (c) 3 63 , (0) 50 t y y e y 2 . (30 points) Find the general solution for each of the following 2nd order linear homogeneous differential equations. (a) 12 36 0 y y y (b) 12 28 0 y y y (c) 12 100 0 y y y (d) 2 9 16 0 t y t y y 3. (25 points) (a) Find the general solution to the 2 nd order linear homogeneous Cauchy- Euler equation 2 11 16 0 t y t y y . (b) Using the method of your choice, use the solution to part (a) to find the general solution of the nonhomogeneous differential equation 2 3 11 16 220 t y t y y t .
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4 . A mass-spring-damping system obeys the equation 2 0 y y y where y(t) = downward displacement at time t seconds. At time t = 0, the mass is pulled down 6 units, and given an initial upward velocity of 8 units per second.
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