0910F-108-02-midterm1-solutions

0910F-108-02-midterm1-solutions - MATH 108, section 02,...

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Unformatted text preview: MATH 108, section 02, Midterm #1, October 1, 2009. 1. Solve y’ + y2 sin(x) = 0. V12 Cévx wk as <1”; {LSZSMOHvO . TLA efim‘lflfivx IS Maui. dx w; Cw‘ :1“ +0 "‘13 " Stanfl)‘ - 33' 2. Find the general solution to the equation 3/” — 8y’ + 12y = 0. ML ML M Serf gr ‘9‘ soL'l‘bK’ (H “PAW, we. {met \ I r a : @‘YALJU me +- H- : Y3.ng ' ‘Krev 4’13 “a; ((1/8r+ll>~erf m choral-errata gide is 0:: rzzfir-HL aquéflhl) W hack are. LRQ. 7L2— $.9ka is hilt?» '1 7L. d7 3. Knowing that y1 = :13‘1 is a solution to :rzy” —— 2y 2 0, use the method of reduction of order to find a second solution to this equation. We. win-(- 31; V“! ~11; k a SgL‘Adn . Li’s r?‘ m 72w. X ;1 :(3 2 N "I , O: X ~15»; ** XV -zv +21 «21 7‘ jz x x dLku 1 Xvu~2v ms, ‘gw his Jayne 4—0 we. "9522‘; X“ _ 2 v‘ " X 2 4. Knowing that y] = ac and y2 = 532(111 x) are solutions to 3323/” — 3xy’ + 4y = :32, find the general 2 ll solution to a: y — 3003/ + 4y : $2. (You may assume that we work in x > 0.) (dis use woe-42:ka 5" “It WWJV' 7%“ “Pd/"200 3‘0: “53"‘VLU‘L '3 “ SOL—kw +0 xzb“’3xU"LL/U ‘73 or how “WWFHJL/‘j 42'“ VS) 5. Usmg an mtegratlon factor, solve the equatlon (y + my)d$ + gdy = 0. H N {M “344 9g —, l+s< ¢ 1:953 5g 1% head» ,5 “3+ emf- rum/lb Lat/4 {7’ “L a K ~ ~ fiamej)!‘ //b? "l‘ ' we” “’ij Q’LKM‘ "Lg—[Kw/‘g: %2‘3V:%‘NK=/*+Xfix Swivw’ raga)” 71% Wk wad—F XI" 1 95/44 / ‘9’ f’x‘l‘,/‘I~?{,s #:25- jv‘kjw'ha,wea W [9493 g“ a “P 6.4: ficng 4931;: x X 50 §¢ g; 4K 7,. Scwxjmxix .2 51<ex+>w -e") «l' 365) : x5e, +j(7) . 4.. K . NmL #vn‘ xa :N ==§é1 xewj cjcjjo" ‘ K —- X 30 W ‘C X 6. Use the Laplace transform to solve the initlal value problem 1, ogt<7r 2; y"+y= { / y(0) =0,y’(0) = 1. 0, tZ7r/2; 2‘ iaujr/(é) Talctflj Lawéu’wtsgfm an lag/14 S'lzs) W £w§ok $2.\ lag—£3 S - —st ’ L {1% Y 7’ "zL 4%) ; J— + (“Q A) — 5 (we’ve? 9'H Scszfl) S1+1 . s g?” w w 3—. at“? + m w —i‘¥s~i € W??? 7. Prove that £{f’(t)} = s£{f(t)} — f(0). w , mt £15m}; 5 #09:ch W— E 4 o (144 ="S£$J{’ V 7. , % w , :— es Qty/m + s3 wee “2/6 0 .3 ‘7 “4(0) 4— S £{§C{); ...
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This note was uploaded on 01/17/2010 for the course MATH 108 taught by Professor Trangenstein during the Fall '07 term at Duke.

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0910F-108-02-midterm1-solutions - MATH 108, section 02,...

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