M334F11E2Sol

M334F11E2Sol - Math 334(Ordinary Differential Equations...

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Unformatted text preview: Math 334 (Ordinary Differential Equations) Exam 2 RED KEY Part I: Multiple Choice Mark the correct answer on the bubble sheet provided. 1. If y ( t ) is the solution of y 00 + y- 2 y = 0 , y (0) = 0 , y (0) = 1 , then the value of y (ln 2) is a)- 7 / 12, b)- 1 / 3, c) 0, d) 7 / 12, e) 4 / 3, f) none of the above. Solution: The answer is (d) 2. Given that exp( t ) = e t , c is an arbitrary constant, and y 1 and y 2 are solutions of ty 00 + t 2 y + sin( t ) y = 0 , the form of the Wronskian of y 1 and y 2 is a) c exp( t ), b) c exp( t 2 / 2), c) c exp( t 3 / 3), d) c exp(- t ), e) c exp(- t 2 / 2), f) c exp(- t 3 / 3). Solution: The answer is (e). 3. A general solution of y 000- 3 y 00 + 7 y- 5 y = 0 is a) y = c 1 e- t + c 2 e t cos 2 t + c 3 e t sin t , b) y = c 1 e- 2 t + c 2 e t cos t + c 3 e t sin t , c) y = c 1 e- 3 t + c 2 e t cos t + c 3 e t sin t , d) y = c 1 e t + c 2 e t cos 2 t + c 3 e t sin 2 t , e) y = c 1 e 2 t + c 2 e t cos t + c 3 e t sin t , f) y = c 1 e 3 t + c 2 e t cos t + c 3 e t sin t . Solution: The answer is (d). 4. If y ( x ) is the solution of xy 00 + y = 0 , y (1) = 0 , y (1) = 1 , then the value of y ( e 2 ) is a) 0, b) 1, c) 2, d) 2 ln 2, e) ln 2, f) none of the above. Solution: The answer is (c). 5. The form of a particular solution of y 000 + y 00- y- y = cos t + e- t is a) A cos t + B sin t + Ce- t , b) At cos t + Bt sin t + Ce- t , c) At 2 cos t + Bt 2 sin t + Ce- t , d) A cos t + B sin t + Cte- t , e) A cos t + B sin t + Ct 2 e- t , f) A cos t + B sin t + Ct 3 e- t ....
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This note was uploaded on 11/29/2011 for the course MATH 334 taught by Professor Dallon during the Fall '08 term at BYU.

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M334F11E2Sol - Math 334(Ordinary Differential Equations...

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