finals06 - 92.236 Engineering Dierential Equations Final...

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92.236 Engineering Differential Equations Final Exam Spring 2006 Please write all answers and all work in the blue book provided. PLEASE SHOW ALL WORK! You will not receive full credit if you do not show your work. Problem 1. (15 pts.) Solve the following initial value problem: xy ± +5 y =7 x 2 with y (2) = 5. Problem 2. (15 pts.) Solve the following initial value problem: xyy ± = x 2 +3 y 2 with y (1) = 2. Problem 3. (10 points) Consider the Frst-order autonomous equation dx dt =4 x - x 3 a. Draw the phase line for the given equation, noting the equilibrium solutions. b. Sketch the graphs of the Fve solutions that satisfy the Fve initial conditions x (0) = - 2 , x (0) = - 1 ,x (0) = 0 ,x (0) = 2 ,x (0) = 3. c. If x (0) = 3, determine the limiting value of x ( t )as t increases. Problem 4. (10 points) ±ind the general solution to each of the following differential equations: a. y ±± +4 y ± +5 y =0 b. y (4) - 9 y ±± =0 Problem 5. (15 points)
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This note was uploaded on 11/01/2008 for the course MATH 236 taught by Professor White during the Fall '06 term at UMass Lowell.

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finals06 - 92.236 Engineering Dierential Equations Final...

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