practice_exam1_solution

practice_exam1_solution - ’7’” 1(12 points Solve the...

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Unformatted text preview: ’7’” 1. (12 points) Solve the initial value problem @_ my alas—zc—lI N 11(0) 2 1. M : qua/11m .J.H ally “ xdx: flax: (1+ “Mlx Tm X4 X4 mE—s’l =335 gig-P )S’JLowla/r IIW dw y dg \L W‘th MC 7356 “L53 ‘3 __ v Jigng ’L *5 j: (x+c) low: a 3 W ,1. HL 3. (12 points) Solve the following initial value problem. You may leave your solution in implicit form. 1 y272$ydw+(£2+2y)dy=0, y(1)=2. «x3 $9 9 $94) 3 x3» 13:3? =5 33:": 313, >< fl j3> {inf/wt, "" .d ,c‘L/JL _L A}: 37,“?le a» 3X __: 32/ 2g Eggzm; ‘fi'wj 1‘) (If: “(X/I" +I1Hj) :5 M X 4. (10 points) Find the general solution of fy’ = my + m/zcg — yz. dv dx «I ‘ / .5 M .5 3w: (1/): Ale—H. =3 U=~Wi(’v/X/+C) x j 5- (10 pointS) Find the general solution of :> Salt): EQWII‘ } dflv—i‘m by 343’s 5*: 9/ M: :5 %$g\g"lgfk§ :> —di;‘;+bt=ex h: ‘4‘» >6 6. (12 points) Slime is growing on the surface of a. 'pond. It doubles the area it covers every 3 days. Initially it covers 1% of the pond. How long will it take to cover the whole pond? ' Vt [:12 (H: f PfiFgPIP 3:» mm; .9 knelt ; a; 720 j (Hus t W fi‘wlé )2 ~2—t 7. (10 points) For What values of a, b and C is it true that l3 3l l3 3H3 il l5 3l 61 b 5”“ lé§]‘[?§]:[0 a] _ 31;}:5 2c=zc—:> enigth 8. (12 points) Solve the general solution to 5.4L 2’1J-0~r&9fij (m—1)($~+2)y”=y’—1, $>2. { L l I u I 7.. .311 _ ‘4‘} {x : “F'— + C 31)‘ (Xq)(x_.1f) 3 : (X4) [564) b X—L V ’\ (Xe?) 6 ‘f'C. Kg) I ‘ *5 J" 15—7” ‘L + c X’H (flit V35, I v V; (xvi +6! 'xJ' 9 X4 I x}! 1 - ._ a r— CI uf+ (fi‘fv) V ' (“W”) ' Cr + xi! 41.42 x 5:1. 33.. __.-_ 1’ Cr 10”: affix" X by! :91" x~7« ; x-» b '2:- Cf’L Xv! x—r ,Lf __><j.. _, .1— adgg (7'3 V > 7 “(xmxwfi Xv} " ’(X~1)L 3) : C! X + (”C')/“ ("4) Jr Cb 9. (12 points) A solution containing 3 g/liter of salt flows in a 60 liter tank at a rate of 6 liters/min. Initially the tank is half full of pure water. The well stirred mixture flows out at a rate of 4 liters/min. How much salt (in grams) is in the tank when it overflows? 36?- mg) a we»; we m: an M. at mm: “Pg/“fink; AM) It W“ “' M“ “'4 ‘9‘“ “4‘ “I? "but am; ms wal’ {WA flit) 1470M V15") -dU:Y’Y‘z,‘ {DJQ’T’} 5'? I it) Vzgo-wt uo =Vm=30 1/sz l 0 45"]; ¢A_ a __ A I“ yr 1 .935??? Crylicva: )3 ,_,4’_é‘\_ gully «18 ISA: l mitt/v IIWI/ l 3 0M 1 3 I :2 : g (15%;) +c .. 336+ IS+C2A 8 > A4 (oh-Ft)?” [é Jig C:éx:§‘5 1H3); effitdt: Off-t)» AEO)':/jhs: D 6 ‘1"4— 3 5 :5 A : (19021“ t) W: 1‘? Mus): 157.9 I ...
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practice_exam1_solution - ’7’” 1(12 points Solve the...

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