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# first-exam - \$0 Math 3041.2 Test 1 D0 anyﬁve of the...

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Unformatted text preview: \$0 Math 3041.2 Test 1 2-29-08 D0 anyﬁve of the following six problems. Show all work. Credi! will be given only on the basis of work Shown. {O 1. Solve the initial-valueproblem 51X: “V“; y(0)=2. , \ air 2x+1 I‘D/25‘5””! o’j-(‘j 1.. /U4l\)0§..3( l —— , l '34l 513’ 52X“. .9” r 4 l + /g I] 1am d c C (tied: €~(2X*frhl+c L _ { Ila. 111 l 1*“ C 3W} “(g-.HZWI] ”I. 1 5 'r “ chr) 1 J L t at 515:5”(2x4-D'3wl) x>-5 4 2. Find the general solution of 1—y+£ = y‘z, x > 0 . lemma-9L" x 0b» 4 l J L 2'3 7% /g lgiléiw 1 '3 ST: 4' :3“ ’ l Cl?— 5; l- U] l V J 1 l‘ n 4‘ L“ K 8:)?- C(k_ 15/ «ilk E X ‘— 5? = 37 at? (11‘ Ax, d!" f 3 2 a. a" ”Fl” {3“ ”‘5‘ J __ (l (12 3 _ / k 5 (x kl—%XIAL/kﬂ Moth 304/ .2, Spring 2008 Test l 1 /O 3. A 60 gallon tank initially contains 30gal of pure water. Saltwater containing 2 lb of salt per gal enters the tank at the rate of 3 gal/min, and the mixed solution leaves the tank at 2 gal/min. How much salt will be in the tank in I minutes, 0 St S 30 ? M M M ’ ‘ ﬁlémfxlw : l 05me 1 x - 3 (”aw-l: ‘< : HEM) 4,9 . . A 3 E - F My GO++—)Ljﬁl ”‘31- i U 1 Z.(3O> :C. l C :.. "" 2(30> —- ._ __ 9% ~ -2 0, “5 i“ g (30%,) . (1:104) Y : ?(3046) ‘20-0) l .16: 2V I 'ZC‘DO)E [(-f J - : {Q 3"," Q(30+{>— _—_._.._ (BO-4+5 (50*{11 V A 3 ILD‘W d—l’ - (939(30'4) "C(l=30>:2('3o§303- \$3. 0 (A (30+é) I l {1mg 450%" PF ”(W—“L “149% 4. Find an integrating factor for xy clx + (1:2)»2 + 2)dy = 0 , and use it to solve the /0 equation. 03”“ y 1 21V, 1 7:3” ' 3*0 a , (9‘17 _./_ 190,147 Y '1 1 “(1 L 07.20 {70*Yfgkg“(3v<j)= gist-1.4131 , J :2 a - I I /’-3 “&/j/:£~/g/'l NJ :ZJ :20 M 321 y ' K .02) El a: i 7:: >231" wig—9,, Sfji; in): 'l {{51); 2 El lgl 0161:0304}; Spring 2008 Tax: 1 [‘0 ,2; Eff [0 5. Solve the differential equation xyg— : 2x2 +y2, x > 0. k x 03th 1‘ o 23. 01% .5113. ‘3' —-G:L' glﬂ?m)h 5 ?J ’3‘ k) 5L}: ’2. *1: E £4 43. 2xt+(?2k‘/l fkd?:.£dk c 1 f X' 4 l9 At 33—50: -?+ 5—2: _ a? 4 7&1 j (1': " :1» /’ tl‘tl‘i- ﬁlkl /'4 “r 39: : 3+3?“ 2‘ 9 “K 11 ‘3: 7 31*09L-(JV A). 2 x , g: ; 1 ~,_. ,95 HF- 71 F“, = -‘ /f ' t, u 5“ '2” It , ’h. / Fl Ehrl’VBCV) L / a 1 (w) 4;” Ar ‘ ‘23. Use Euler’s method to ﬁnd approximate values for the solution ofthe initial-value problem Edi: 2x(y+l), y(0) =2 atx= 0.1, 0.2, 0.3, 0.4, 0.5. Give numbers to 4 decimal places. Compare these values with the exact values y(x) , and compute the percent error En =100[y(xn)— yn]!y(xn) to two decimal places. ; I (I - i \ r \ “\ r x“ 91(c2f-l}QMJ‘LU'QAOEOO c 3.1 g'ogl(QC'RIDCZDé*/))E‘()LQ-l‘l’Q-Ll /92de L]! / a a, .1‘ :uavtul (.13. l 2.137 (it )C l D l 3’5 r... {L/ t/ ‘1‘ __ .2 ’tﬂvﬁq r (70‘?) (’2.°>73‘>‘(4 0X1) 1 (j .¢ \ C. 6 2 J“: I.“ L _/ k 3 1 C C 'l\ } X17) {-3 H C :a a '— 3 6/ —— l Math 3041.2, Spring 2008 rm; f z (i f f,- 3 ...
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