M334exam1Su10solutions

M334exam1Su10solutions - Math 334-1 (Ordinary Differential...

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Unformatted text preview: Math 334-1 (Ordinary Differential Equations) Exam 1 RED KEY Part I: Multiple Choice . Mark the correct answer on your scantron. Each question is worth 5 points. 1. Which direction field is correct for the equation y = y ( y + 3)? a) b) c) d) e) f) Solution: d) 2. Which function is a solution to yy- sin ty = t 2 sin t cos t ? a) y = t cos t b) y = t sin t c) y = cos t d) y = sin t e) y = t 2 sin t cos t f) None of the above. Solution: b) 3. Let y ( t ) be the solution to ty + 2 t 2 y = 2 t 2 y (1) = 1 What is y (2)? a)-2 b)-1 c) d) 1 e) 2 f) None of the above Solution: d) 4. Solve y = 3 x 2 y 2 , y (2) = 1. What is y (0)? a)- 1 8 b)- 1 9 c) d) 1 9 e) 1 8 f) None of the above. Solution: d) 5. A 200 gal. tank initially holds 100 gal. of water containing 1 lb of sugar per 10 gal. If a solution of 1 lb of sugar per 5 gal. is added at a rate of 2 gal/min, and the mixture is drained a a rate of 1 gal/min, how much sugar is in the tank when the tank starts to overflow? a) 20 b) 27 c) 35 d) 40 e) 45 f) 50 g) None of the above. Solution: c) 6. Consider the initial value problem yy + t sin( y ) = 0 , y (0) = y . For which values of y is a solution guaranteed? i) y = 0 ii) y = π 2 iii) y = π a) i only b) ii only c) iii only d) i,ii e) ii,iii f) i,ii,iii Solution: e) 7. Consider the initial value problem given by ( t 2- 1) y + ln | 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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M334exam1Su10solutions - Math 334-1 (Ordinary Differential...

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