Quiz5Soln - Math 170, Spring 2009 Instructor: Timothy Lewis...

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Unformatted text preview: Math 170, Spring 2009 Instructor: Timothy Lewis TA: Tamara Schh'chter (Section A01) QUIZ 5 Student ID: Show all work for credit. 20 pts possible. 1. (3 pts) 'Write down the solution for the initial value problem. (Note t z 1 in the initial conditions) d2: dt = —2x, x(1) = 4 2. a. [4 pts] Show that x = 0, y = 0 is a steady state (i.e. an equilibrium point) of the system. if? = O+°>(o>=o 2m a): ‘ :3 (DNA is o\ 93(03 .\ O = O 3%€&C\g b. [4 Write the system in matrix form. 315* l5>< it fiig ll c. [4 pts] Assume that the eigenvalues A1, A2 and corresponding eigenvectors v1, v2 of the matrix of coefficients are A1:_2,’U1:(_11> and A224,U2=(i) Write down the general solution for the system of differential equations. X“) “2+ l we ( = C/\€/ "t C26 gm ‘\ d. [Spts] Find the solution of the system for the initial condition x(0) 2 2, y(0) = 0. Describe what happens to a: and y as t ——> oo. ll flea —\y C A“ \ Q % CUB JD~§>PO ...
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This note was uploaded on 10/27/2009 for the course MATH 17C taught by Professor Lewis during the Spring '09 term at UC Davis.

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Quiz5Soln - Math 170, Spring 2009 Instructor: Timothy Lewis...

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