HW13 - Math 17B p Kouba First—Order Linear Differential...

Info iconThis preview shows pages 1–16. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 14
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 16
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 17B p Kouba First—Order Linear Differential Equations 1.) Solve the following first-order linear differential equations. d.) 5323/ + my :1 e.) (1+m2)y’+xy+x3+a::0 f.) 5101/ + (1 + :E)y : 6“” sin 23 dy {wag—11+»? h.) y' 22y+$62x and 31(0): 2 i.)cosx-@+ysinx=1 P d]? 1—6—29” - I — J-) y +y— ————ew+e_m k.) (1+x)y'—9:y:at+cc2 d 2xsinx.—y+y0083 =1 dac x 1.) cos x)’:331<'5“7( a lxy:M(X(+C/} a) ((+x3/fl—L—Xj4—x‘34rx: 0 —-——->- (wxzjjky xj : ~x3~>§ x» z._>.<.. yzw 1-x <>l+x+><A (4—x-’~ l K M y H 4*- f” ' MK j W ENC MK conx-W M . J7: Q] :MK’3’? I cov‘x mykx a Math 17B Kouba Worksheet 2 Let S represent the amount (in pounds) of salt in each tank at time t minutes. Find a formula for S for each of the following and then answer the particular questions. 1.) A solution containing 1 / 2 lb. of salt per gallon flows into a tank at the rate of 2 gal. / min. and the well-stirred mixture flows out of the tank at the same rate. The tank initially holds 100 gallons of solution containing 5 lbs. of salt. How much salt is in the tank after 10 minutes 7 after 1 hour 7 How much salt do you expect to be in the tank as t gets infinitely I? 2.) Pure water flows into a tank at the rate of 4 gal. / min. and the well—stirred mixture flows out of the tank at the rate of 5 gal. /min. The tank initially holds 200 gallons of water containing 50 lbs. of salt. a.) How many gallons of solution are in the tank after 20 minutes 7 b.) How much salt is in the tank after 20 minutes 7 after 2 hours 7 c.) How long will it take the tank to be empty 7 3.) A large tank holds 100 gallons of fluid in which 10 pounds of salt is dissolved. A mixture containg 1/2 lb. of salt per gallon flows into the tank at the rate of 6 gal. / min. and the well—stirred mixture flows out of the tank at the rate of 4 gal. / min. a.) How many gallons of solution are in the tank after 10 minutes 7 after 1 hour 7 b.) How much salt is in the tank after 10 minutes 7 after 1 hour 7 c.) In how many minutes will the tank contain 40 pounds of salt 7 (HINT: Use a calculator with an equation solver to solve for t or just estimate the solution by trial—and—error.) 4.) Beer containing 6% alcohol per gallon is pumped into a vat Which initially contains 400 gallons of beer at 3% alcohol. Beer is pumped into the tank at the rate of 3 gal. / min. and the well—stirred mixture is is pumped out of the tank at the rate of 4 gal. / min. a.) How many gallons of beer are in the vat after 10 minutes ? after 1 hour ? after 6 hours and 40 minutes ? b.) What is the percentage of alcohol in the vat after 10 minutes ? after 1 hour ? c.) When will the percentage of alcohol in the vat be 4% ? (HINT: Use a calculator with an equation solver to solve for t or just estimate the solution by trial—and—error.) wax-{W l 3W ’ MSMW_O{WmMMW/f. 1,) 1?, : @mIm/~LKWOM) M I : (3.2% (M4 _ SW- (032:? a M W (Obj/we M AS _ ‘1, _,_., ‘ _ Mfl M '( 503 31—553 615-8 {—LC, 044/31. ~(;'—‘-O/W\/;A/L. 8:61/u>1._.’ MLFS‘iW ‘éiédfflfi/‘j __.,. 6/ ~ 6 LS _ "390% ___., [“ 5'0 ” 6/ a ...( é ( _ 61 “'5 —-” (x *5/03 730: "(4/ 4/3 H (Va/€60 -———» .é—aoo {—voo :— 50» qféfivw]: 6’O~ 45(0) -EKOZOZ’Efl; _\_ ~ -MM- Xx, 0(WMMQXME 5:11;: OM) : 014:14fi. 51/64.- 5 goo-+M)<% ‘5 12-”?S __., __\_ _ #5 M- ’ XOO—‘t' SS 0‘5 ” 9200+ GDP—3’ MS 3 5M<X00—%)+ (1/. M / Mfotgflmfloo—PQ ._.~, -’ 0 CZMKOv/Q/ngooéz/Qm(ai05~ ——9 I Q, C M (Co/L100 000 000 _*' / / M8: (M Ca00~fJ+MCm>fi 5’ / /(/ M5: MCX00~+2 +14 ij—a C 6, b/ l S : L200~+) (g/qécaoocjooo) __3 — ( " 00 ooo 000 G2/“( / / (zoo~‘é]r “ 174/ v OW) L; 1w. (e Kg. ~ 311” M. We. m. 100+ (2%?«4, M, S 4; ~ (004—524;. 3 fl 4 - __ Ade)? JMAQO7 {oo4va—E~ '3 ~ 3 (F’W O > 100+ M 4'” L/QMODO‘F 2‘6] 63 WC = C 2 2%Czoo+a~é) M Coo+1+)9‘ EL '1 fl Cleo—(r 5.1—6) 9: g ‘3’ (002‘ Clo) : JiC(oo/3 ————¢ C: ~quzoo)9\: “4109000?- -‘*> 000-921(7)? S : iQoo+g~ej 3~ 400/ 000 ,7 I 4/00 000 ._ _____A_____ ‘ : “500047.252 000+ affix J a.) TALMW é-—<4: afl/M (2,] f: MM —_ {004 02(on : lac CL) fléeo/w‘m: 100+XC©71 02020 b] ‘63 {OM/WA 0 1 LORD “ q 0"000 $52 M Ma ‘9‘ thé/ (*1) f: QOM q o 00 oo ézigaaoj~ thof’mum Q.) 51401434 : 47/0: .1.0oo4;yé)~ 35:33 __> (100+&~é)7\ (/0: 50+{ ~ goo 000 —> (1004491 M ~ (04:67 ___7 C ’ a Gomaéfi W} fix ads M d$ “fix _ 5 239m. (4 2&.W) qoo~~€ M. 4 o.(8>—_ qw‘f- S 4 - .15? q00._._~g S~ O —- ‘ FM-OW + q 330%“ (in-MM ifl=e =€ ~ CMC‘E‘QOOJ ‘4 C%‘qooj‘qg a v "4 AS "f , *9 g m) .E# «(@4095 V0.23 eaqoo/ —> D [CE-«oojflfisj 2'. 0,18 C‘é:~ ((00 ~q .__~, Cwé—qoofffs : BO.(5C€~L(00]~QJL>(—__, «,1 o. 0Q: ~ (A ~ 4’ : (5’6ch @0023 C/ .—7 C 4(00q E *5 q —. _ ‘3 (7x 66—400) 3 - o 0% (JC—qoo) »~ (/00? —> S: "'0 662 {2.4/00 - ‘3‘ ‘6 Moo V C j 4/00“ C a ...
View Full Document

This note was uploaded on 02/17/2012 for the course MATH 17B taught by Professor Kouba during the Winter '07 term at UC Davis.

Page1 / 16

HW13 - Math 17B p Kouba First—Order Linear Differential...

This preview shows document pages 1 - 16. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online