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Unformatted text preview: MATH 216 FINAL EXAM April 23, 2010 Please write your name: 4 points Section: ____ _ The test contains 8 problems worth 100 points total. To get the full credit you have to show your work. Page 12 contains a table of useful Laplace transforms. Problem Points Score 1 12 2 12 3 12 4 12 5 12 6 12 7 12 8 12 Total Typeset by AMS 'lEX 1 Name:  (12 points) 1. Problem. Find the solution x(t) ( ) equations ' Y t to the system of differential x' = 3x 2y y' = 4x y satisfying the initial conditions x(O) = 1 and y(O) = 1. I I\ f X = 'j x' ll I j =  2j 'j I  3:(t 3j  )' tl 1 I _. Q Lj +S_J:::::. '2. 5 0 r  2.,t =... 'L (r1 \ t 4 0 r t ± l::) =  .e, +. c.n L1 2 L 2..1 y: ::::. t L.J ;..{ L L.f Name: ____ _ (12 points) 2. Problem. Find all critical points of the system of differential equations for functions x(t) and y(t) below and determine their stability x' = xy  3x ::::. t y' = X + y2  4. 3 X ( ':J 3 0 ::::0 (i) x ::::0 , = 2 (::ll X= OJ ':) :::: 2_ (Lll) LJ=3 ><==!::> r l [J; 3 0  Lt<o) + s = 0 b tf + &> '). + s; =: 0 ::::0 3 Name:  (12 points) 3. Problem. Match the systems of differential equations for functions...
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