M334exam1Su06solutions - Math 334(Ordinary Differential...

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Unformatted text preview: Math 334 (Ordinary Differential Equations) Exam 1 KEY Part I: Multiple Choice Mark the correct answer on the bubble sheet provided. 1. If y ( x ) is the solution of y = sin x cos y , y (0) = π , then the value of y ( π/ 2) is a) b) π/ 2 c) π d)- π/ 2 e)- π f) 1. Solution: b) 2. Which of the following equations are nonlinear and second order? a) y 00 + 3 y + ty = sin( t 4 ) b) y + y 2 = 0 c) y 00 + (sin t ) y = 0 d) yy 00 + y = 1 e) ( y ) 2 + 2 y = tan t f) y 000 + y 2 = 1. Solution: d) 3. Find the correct integrating factor for the following differential equation: y + ( cotx ) y = x ( Hint: cot x is cos x divided by sin x .) a) e x b) e- x c) e 2 x d) ln x e) 2ln x f) cos x g) sin x h) e cos x i) e sin x j) x . Solution: g) 4. An object of mass m kilograms is thrown vertically upward with an initial velocity of v meters per second from an initial height of y meters. The earth exerts a downward gravitational force on the object of magnitude mg , where g = 9.8 meters per second per second. The air exerts a resistive force on the object of magnitude k | v | , where k is the drag coefficient with units kilograms per second. No other forces act on the object. Let y ( t ) be the height of the object in meters after t seconds have elapsed, v ( t ) be the velocity of the object in meters per second at time t, and...
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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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M334exam1Su06solutions - Math 334(Ordinary Differential...

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