182631 - (57”(11‘ 1 Find the general solution of...

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Unformatted text preview: (57”,:(11‘ 1. Find the general solution of 33;” -— 431’ + 3y = 0. ‘ lg/ EVE-HM 3 r 0 ( Ail/@Mgfi) (t. ‘33—; t '35:} 9E ‘3 , v; m " “/p ac I \I; g N’ M 1 M . #: C,£ Co‘s/4‘67 +(,€ San/1;? 2 i gt / at]? r“ “CH/i «‘3 ‘ M? I Ltg M427K Exam 1B Name 303mm momma NO NOTES. NO CALCULATORS. 2. For the autonomous equation 3/ 2 2y — yz, determine the equilibrium solutions, classify their stability, and sketch a few representative solutions. , / , r7 , y ‘5 O “A? 2*“3’ ‘42 3' C) ukk <3? 0 4C ' Vi") 993’ ‘11 a l I , ' I \lx ‘ Q / so \ V5 3' E21 kgmfitoi‘mOJ/LB SAFKWU 3 A large tank initially contains 75 lbs of salt dissolved 1n 1000 gallons of water. Pure water is pumped into the to tank at a rate of (fig/align The well~mixed solution is pumped out at a rate of 3 gal. [min Write an IVP whose solution gives the amount of salt 1n the tank after t minutes (Don’ t solve the IVP.) am A , ‘ (‘V "J 1 \f’ . (DTA A“ w 4.4’" p ,9 \fr ”8&4“: U03}: 1000 : 31441 EB. » ,égfil ‘QLOB = Cli; gt+1000 ) 4. One of the following DE’s 1s exact Figure out which and then solve it. ‘ M, K A. (my+1)dm+(xy—1)dy=0 -. 3, MT: Xff IW- ‘/ "h l x B sinzcosydm—sinycosxdy: 0 \n ; N 1‘ Mg mum .‘ f MK; . ,.,,- >4 (:5 Dysinx+scycos:r) dw+(xsinx+1) (13;: 0 ’ WA”, M7: Sihx *- xcosx NX: KPX 7 MA“ "7' Q: gvymnx +Xb3f0§>irl¥ \0 1.1»>< (\U/ (“X W:~U\CO$K + U) XCOSXA“ (\U: \é‘i (\j: 43an +‘r‘l~ ,/ ‘x lfll \— \_‘rh- 7:3 )< 6“ n X /g fiqfix f .1 + (one ' ” ”‘Anyfitz\ \ ,‘ . U2 :— (fig/(95;!) + \{XSrWfil {it/(.USX #hui) / 1*” CW (2a -w /Qeif 0dr. flak “A ._ (puss {@161 f 9 $4 l W ' $1:on + 35“.! 0% / hw- \J Y 1‘) \J «(1+ 422m A (-t , 2‘ E133 '4'“:th , 0 5. Consider the‘flflifit ‘j‘ 1)y” — (t + 2)y’ + y «T- O, y(3) = 2, y’ (3) = 0 and note that yl i 5: is a solution to the DE. Find the largest interval over which a unique solution to the IVP can exist. Then use reduction ofvorden to find a second solution. Show that the second solution is linearly independent over your interval and then give the solution to the IVP. ' , + \ \ Ji u \‘, ‘51: v5V \l‘: \M Mel C (“u") Y9? 3+(v\4\1\)»€(\1w.)7, L ' f ‘94 (V’r Eva/X -~‘ V"; CE ”5(5JrW‘t9VW-V - (walk/Wow» Jr \JeA : o <15 "L DLV't 3‘» 4V“) ”(‘t'ldXVtHOA’ \l C (D ) _,\ f . ‘ ,,, «r». ,2: \ ,- ,\j GUM ‘e-fig \ \jf m “I V + JrV‘ + t \J‘ Jr eély/lm/ ’25 fi l ‘7" “V; ’ C W 39“ H + \5H \\\ 4 (75/93 \ Z , 3/9.?“ ‘ 1‘ \h, \‘\%Q\{/?: - 5 A») W ; at (+9) , um I?» , t Xe’g’lfi) \ ‘t {— /4\“ \{L’ e "J .L \N {+7 __..\ i we "(’L'C “QC 3 67. \/> ,g&-E€t [email protected] \ f ‘l' /’C /QC*\\(\ Lt\\ VJ L++l>$ w” — W 6.7"" ,2 6 (0( AZ 8 Jr»! L (/W {OifngrCe/l; [leM// :27 -t’\'\ \ JC 4 1an +l)\ ‘€ 5) W o v ’t , J; 6340 C + ”6 x x~ ““m \ en mg ~ (w: '3 New? 8‘: ...
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