266StudyGuide

266StudyGuide - 1. If y ( t ) = sin 2 t is a solution of y...

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Unformatted text preview: 1. If y ( t ) = sin 2 t is a solution of y 00 + 9 y = f ( t ), then f ( t ) = A. sin 2 t B. A cos 3 t C. 0 D. 5 sin 2 t E. 13 sin 2 t 2. If y = y ( x ) is the solution to dy dx = 4 xy 2 + x 2 , y (0) = 4 , then y ( √ 2)= A. 4 B. 16 C. 1 D. 2 E. 2 √ 2 3. The general solution to x 2 y + 2 xy = e 5 x is A. y = 1 5 e 5 x + c B. y = 1 5 x 2 e 5 x + cx- 2 C. y = 1 5 x 2 e 5 x D. y = ce 5 x E. y = 5 x 2 e 5 x + c 2 4. The solution to the problem (2 xy + x 3 ) dx + ( x 2 + y 4 ) dy = 0 , y (0) = 1 is A. x + 1 5 y 5 = 1 5 B. x 2 y + 5 y 5 = 5 C. x 2 y + x 4 4 + y 5 5 = 1 5 D. x 2 y + 4 x 4 + 5 y 5 = 5 E. x 2 y + x 4 + y 5 5 = 1 5 5. The solution in implicit form of dy dx = x 2 + 3 y 2 2 xy is: A. x 2 + y 2 = x 3 + C B. x 2 + y 2 = Cx 3 C. x 2 + x 3 = y 2 + C D. Cx 2 = x 3 + y 2 E. x 2 + y 3 + xy 2 = C 6. Which of the following best describes the stability of equilibrium solutions for the au- tonomous differential equation y = y (4- y 2 )? A. y = 0 unstable; y = 2 and y =- 2 both stable B. y = 0 unstable; y = 2 stable C. y = 0 and y = 2 both stable D. y = 0 stable; y = 2 unstable; y =- 2 stable E. y = 0 stable; y =- 2 and y = 2 both unstable 3 7. Solve the initial value problem y- y = e- t with y (0) = a . For what value(s) of a is the solution bounded (i.e., not tending to infinity as t → + ∞ ) on the interval t > 0? A. 2 B.- 1 2 C.- 1 3 D. all values E. no values 8. Initially a tank holds 50 gallons of pure water. A salt solution containing 1 3 lb of salt per gallon runs into the tank at the rate of 5 gallons per minute. The well mixed solution runs out of the tank at a rate of 2 gallons per minute.runs out of the tank at a rate of 2 gallons per minute....
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This note was uploaded on 09/14/2009 for the course ENGR 126 taught by Professor Oakes during the Fall '08 term at Purdue.

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266StudyGuide - 1. If y ( t ) = sin 2 t is a solution of y...

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