math252b - Math 252 Exam 1 September 30, 2008 M ial P‘...

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Unformatted text preview: Math 252 Exam 1 September 30, 2008 M ial P‘ Musial Name Instructions. Work each problem on the exam.. Where on are aske to solve an equation, make sure to find all solutions. Show all work. \ 1. Solve the DE. (I? I 7 Z —. J y(1 +332) 2. Solve the DE. 3/ ~ 3y : e2”. 3. Solve the DE and give the largest intervals on which a solution can exist: xy'+y=a:3. 4. A tank initially contains 300 gallons of saline solution with salinity 4 lbs of salt per gallon of solution. Solution having salinity 2 lbs of salt per gallon is pumped into the tank at a rate of 2 gallons per minute, and solution leaves the tank at the same rate of 2 gallons per minute. Find the function A which models the amount of salt in the tank at any time, and find the amount if salt in the tank after a long time. 5. An invasive species is introduced to an island. Its population grows according to the DE dP dt Assume that P (0) = 1. Sketch a graph of the solution curve and discuss the limiting population of the species. It is not necessary to solve the DE. = P(400 — P). 6. Show that the differential form 2:53; day: + (y2 »— $2) dy = 0 . . . l . is not exact. Multiply both Sides by the integratmg factor —2 and verify that the 9 resulting differential form is exact. Solve the DE. 7. Solve the DE e _ 1— I ~ y. d]: a: + y subject to the initial condition y (0) = 1. 8. Solve the DE dy ,_:r:2 ——y—ey. d3: 9. Solve the DE (x—y)d$+(av+y)dy=0 // x} spzmmaéb L, 3: L0 M (W‘) ANS: b? I; Sbfléméw 3 332. 3 ,2S___ M gfl—Mfi) Kw) 0” Wt; ' W V5.9 u= IH<Z M : Z’XOLx Sb 1 é/4({+Kz) +c 2 2 , L52: /én(/-+>c‘)+c' fictm Mmfias’z W58 Wm! «LU— Sa‘lwefle ‘9' awe” Ans: VDE IN” WM I‘M/29% 74:74. 3K 17m): 6" Q 6* ‘jfluQ’PEY-z fl yaw“!— C8376 {mm/4 M (4 0%: 4 =1 flax/AM; MMIPM-K J mM salt/44w hwy 4% “Emir: «+71% Sam {Eula 41 am,” paw/Wu, PM m AM” AN) wlvtok W, Wamamfdfl swam m “Ian/(M any 4-MAQ) osM 74AM“ “WU/#‘i W mm vleK AVA/AVA /o/\j ’4’” an!) 23;: I‘/\’_‘ {gawk 00+ {ad-QM“; QWmsmm‘.Q IMCMIZW: 4/ ]; TL 7) A/ W 343 '4 (906» Q rpm O 60 ’1 M Spec/lg; 3 A. ‘3 ’tz’ ' T A 5 fl mu W005 bL 5w a PNS‘e Akfij/‘qm meanfl/aw m PDPUIAJ‘% Mil W "\va ‘wto, $W P6)=/ (WW , Cold-Cow Cup“ ((90le /;'1<c 414,9; a Lomsflc C URUG. (a) \Qrm 15% 61% +-/§11~ >8) M : o 53 Afiemu, Mu H—x‘plg Lav-n sup; wng (“4” 9‘3 ammmg WWW Cami-H7 VFW-Raj 74m (5 were? A»; m{)qj)?1¥'1 MAC/j]: gQ—XZ Mg 2 2X /V,C c , 2v Nave-MM ~....... .«M.» ,._,..._ mUIFJ—‘kP/wj 59 3,2 m bows/>0: % 4) éale/M D? 6&7) AW +'/W?é¢/ '10 144$: «(é/m f5 mgf QVaCf/ «Aw-4 fs A’WWU5 1.- J39 j: ax abs} 3 09406 + X0644 (VA!) )c/élyd + /¥”+ Uwfl/W 10 {K F ~+Wyi2du + szdx + 60* 0277 dx -+ (58+ L/X‘QjJt/k : O uxzd“ :4) x( W2) M + X2<1+ULQA =0 K; Jr Hui 00" 5‘ ‘3 .151 : AX 1L M‘flzmu + m4” U 4’ ...
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math252b - Math 252 Exam 1 September 30, 2008 M ial P‘...

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