T4FS2003Math204SecC

T4FS2003Math204SecC - -1 4 2 2 1 1 1 1(18 pts a Classify the origin as a node saddle point spiral point or center b Classify the origin as

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Math 204 Swift Exam 4 Fall 2003 Dec. 10, 2003 Name______________________________ 1. Determine the value of c so that the set of vectors is linearly dependent: x c x x ( ) ( ) ( ) , , 1 2 3 2 1 1 1 2 3 7 8 = - = - = - (8 pts) 2. For the matrix , find . A i i i = + - - 2 2 3 4 0 3 15 A (6 pts) 3. Rewrite the differential equation as a system of first order equations. Clearly indicate which equations are in your system by placing a box around them. ( 29 2 3 5 0 4 y y y - ′′ + = (12 pts) 4. Find the solution of the initial value problem: , . ′ = - - x x 5 2 4 1 x ( ) 0 0 2 = (20 pts) 5. Find the general solution of the system of linear equations: . ′ = - x x 1 4 1 1 (18 pts)
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6. Given the general solution of the system of 1 st order, linear equations. x c e c e t t =  + -
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Unformatted text preview: -1 4 2 2 1 1 1 1 (18 pts) a. Classify the origin as a node, saddle point, spiral point, or center. b. Classify the origin as asymptotically stable, stable, or unstable. c. Sketch a phase portrait (several trajectories), labeling the trajectories of the system corresponding to and . c 1 = c 2 = 7. Given the general solution of the system of 1 st order, linear equations: x c e t t c e t t t t = +- 1 2 3 3 3 3 cos sin sin cos (18 pts) a. Classify the origin as a node, saddle point, spiral point, or center. b. Classify the origin as asymptotically stable, stable, or unstable. c. Sketch the trajectory passing through the point (-2,1) when t=0....
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This note was uploaded on 01/24/2011 for the course MATH 204 taught by Professor Staff during the Fall '08 term at Missouri S&T.

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T4FS2003Math204SecC - -1 4 2 2 1 1 1 1(18 pts a Classify the origin as a node saddle point spiral point or center b Classify the origin as

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