# exam2W10sol - MATH 216 SECOND MIDTERM EXAM ~oV ~,01-1...

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MATH 216 SECOND MIDTERM March 22, 2010 EXAM ()' . ~',01-1 ~oV Please write your name: ______________ _ Section: ----- The test contains 8 problems worth 100 points total. To get the full credit you have to show your work. Problem Points Score 1 12 2 14 3 12 4 12 5 12 6 14 7 12 8 12 Total 100 Typeset by AMS- 'lEX 1

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Name: ------- (12 points) 1. Problem. Find the solution y(x) of the differential equation Y 11 - 4y' + 5y = 8 COS X that satisfies the initial conditions y(O) = O, y'(O) = 0 . . 1/ !I I c -0 v - '-~3 -r v _:;; - / 2 x: L'>< r Jc :::~e_ ~"<:~c._ e ./.Jtr-LX: Yr ~ A co::> x + !3A/" x (- A """'x- - t? fl,;., _,,J - 'I {- A s ;, '< r ']: cv::J-1) + ~/A c,nx _,. }5J/. ., iJ) ;::; 6 (_cY.J'x -A-'-1~ 7'-5'A= g -8-tLfA -r~B:: 0 A~ I ¥A-4B::::-8' tt A -t- LIE ~a Zx 2x: J == <:I { ~ ?( ..-~- C 7 (_ ..,.6 /n,;x -1- 0 K ....- .s ",. ..., >c j ( o ) "" c, + I ~ 0 c, = -I 2 2x <x . y.!!o) = C 1 e. Vf><- <:. . 1 e Al;,.x lx f- {_'1 .f_ ~X _.-- ~ X - .;;::. .2c, -r c&- I = 0 Cz .;:: 3 7.~ 2 t C-n K -f 3 .(__ ~/n)( r (,n K_. ~k 2
Name: ------------------ (14 points) 2. Problem. The position x(t) of a mass on a spring immersed in a viscous fluid is described by the equation x" +ex'+ lOx= 0, where t is time and c is a positive number characterizing the viscosity of the fluid.

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## This note was uploaded on 02/08/2012 for the course MATH 216 taught by Professor Gavinlarose during the Winter '02 term at University of Michigan-Dearborn.

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exam2W10sol - MATH 216 SECOND MIDTERM EXAM ~oV ~,01-1...

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