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AK-MATH225F10-WS5

# AK-MATH225F10-WS5 - MATH225 Fall 2010 Name I ﬁx 3...

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Unformatted text preview: MATH225, Fall 2010 Name: I ﬁx 3 Worksheet 5 (3.3, 4.1, 4.3) ‘Section: 6c? U (0" For full credit, you must show all work and box answers. 1. Three tanks contain brine7 as shown below. Pure water \ 2 gal/min [/‘1. ix. R fﬁﬁgai \N ,«f Mixture Mixture - 2 gaiiamin 2 gat’min Mixture 2 gab‘min (a) Use the information in the ﬁgure to construct a system of differential equations for the amount of salt 2:1(t), 2:205), and \$30,) in tanks A, B7 and C, respectively. A)“ - (DMZ) ﬁgoﬂz) a? a}: : (\$62,) ~6—532—Jaa we 42%» era) 2H; ‘T’k; olém ~0me on?“ 'P/osk ’CLw {RM/:5, 2. The following system of differential equations is encountered in the study of a special type of radioactive decay series of elements: dx — = —0.12: dt = l a = 0.1x — 0.05y “I it : 713LZOL I )‘7—27 ft i ___‘E -_‘f;é CwiiiJra‘gd 2241520 ~b ': 3. Solve the fmﬁTg systém o i erentia equati 7 :— ~Ho eg+Cﬁ° Dowoflzp'i 70») = #0 11:0 (Hint: Use solution techni ues from 2.2 and 2.3. i '75 +H& 5 X Dﬁajr‘ﬁ’y 01 Lab- KQS)='% and 7L0) :10 . ”\\ WES 75:57 alx .y. ~ "5t: 2::th '27; /Z>< ‘l' (’00 7. 7 L sttljt 5013’) ET; :Z)< Hwé 4016 3%: +61) X L l00a grzalt at C M Lt) I a 3 6 zié/O KTLZt 4. Given the second-order linear, homogeneous differential equation 4y” — 4y’ l- y = 0 and the functions y1(\$) = y2(w) = 376% (a) Verify that 311(17) and y2(\$) are solutions to the given differential equation. _% A , = X a 7 I : C 2 (7/; L 4!. _L ~24- / , 2. +7 La?” 7' I : LC?— 7” - G 2/ A x L _ 7 ~ :r'é‘z twaew—e , x , .x - A 1 % L} // -L17/ +):"l{—LIF&L)~L’ZZC +62 L-lyll~l-l7"l’ “16::11’6’) 7 Z O r i nq (aéJ’JzK/éz‘lx’ié 7i Lx) 7'5 (/L 50/0500. 7106215 Q galJClOﬁ (b) Verify that y1(;L) and 112(32) are lineraly independent using the Winskian. 7; X. i A) .. 2 CL 1 .5. I 'Z 2 A L 3:6 Z d + a 6 1L 1 .21 A L 7. % : é?“ C Z "l/ £612— _ 2/6 a X X :: eré—icx—éa :5, i0 zLX) / LAX) Mfg, llocef'l7 lﬂdlcpcﬂdcrrt (c) y1(a:) and yﬁwﬁorrn a fundam ntal set of solu ' general solution. ) he linear homogeneous differential equation. Find the -c, L A 71X) ’ z 6?“ +Cch+ %YOZ 7L0): c.=o 7 ’(o) 2 % Matt) 1/ IX [700:Xc17' 5. Solve the given differential equations or initial-value problems. m X’ (a) 2yl+3y=0 / (C) 2y” — 3y'+4y = 0 / Zmz«3»,+tl=o SIM—H‘KH‘ME V 3,: IE_;_+_1§L T " H ’" L: “V“? ‘ ~31 EL ; Bx‘ 1L p \ a”: L *‘H ”:5?ng qéwamésmw 7 : C163\$Co§ (d) ——6—+9y=0, 3/(0).27 y(0):0 / 7’C (\$352 day ,3 5 \ ML'Gm-FC’IZO 7’ZEC,(:BX+CL</ X+BCZ2<£52< lm«3)z‘ :o 7(0):"C7FZ 7’[o)‘—3Q,+CZ:O \ I L C2,: *3ci:é m =3 7 :C,05X+C;[email protected]} Iiiééw‘ QM: (e) jig+9y=0 / 7:5h"Y W , ~~7 mZ+CL_-O I \7'ZC,CQSLBX) +'CZ/5FQL3%> 5: m7. : i q ‘ M_*__.~.v, _ h M 1 1 F9— : ‘f 3 ( ...
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