examfinalW10sol - MATH 216 FINAL EXAM April 23, 2010 Please...

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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 (r-1 \ -t 4 0 r t l::) = - .e, +. c.n L-1- 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 - L-t--<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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examfinalW10sol - MATH 216 FINAL EXAM April 23, 2010 Please...

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