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

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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.)[email protected]+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 ...
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HW13 - Math 17B p Kouba First—Order Linear Differential...

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