M334F11E1Solutions

M334F11E1Solutions - Math 334 (Ordinary Differential...

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Unformatted text preview: Math 334 (Ordinary Differential Equations) Exam 1 RED KEY Part I: Multiple Choice Mark the correct answer on the bubble sheet provided. 1. Which direction field corresponds to y = 3- y ? a) b) c) d) e) f) Solution: The answer is (e). 2. Let y = ( t ) be the solution to y =- y + b, y (0) = 1 . For what values of b is lim t ( t ) finite? a)-2 b)-1 c) d) 1 e) 2 f) for all values of b g) for no values of b Solution: The answer is (f). 3. Which one the following functions is a solution of- ( t sin t ) y + y 2 = t 2- t sin t cos t ? a) t cos t b) t sin t c) e t d) t 2 e) t f) ln t Solution: The answer is (a) 4. Given the differential equation t 3 y + ty = te 2 t , what integrating factor can be used to simplify it? a) e t 2 b) e- 1 /t c) 1 t d) 1 t 2 e) e 2 t f) None of these Solution: The answer is (b). 5. Solve y = ty, y (0) = 1 . What is y (2)? a) b) e c)- e d)- e 2 e) e 2 f) None of these Solution: The answer is (e). 6. If y ( t ) is the solution of t 2 ( t- 3) y + y = sin t , y (1) = y , then the interval on which the solution y ( t ) is certain to exist is a) (- , ), b) (- , 3), c) (0 , ), d) (0 , 3), e) (0 , ), f) depends on y ....
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M334F11E1Solutions - Math 334 (Ordinary Differential...

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