SolutionsMidterm - MAT 212 Midterm Exam Name Student Id 1...

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Unformatted text preview: MAT 212 - Midterm Exam February 23, 2010. Name: Student Id: 1. o (15) If (1,5 and c are > 0, Show that every solution y(t) of ay” + by’ + 03; z 0 is such that limtnflo y(t) = 0 o (5) Give one example of a linear second order equation for which y(t) = 0 (constant zero function) is the only solution such that limt_,+DO y(t) = 0. - .f ' ' . - - Z @ /AJL (guacémisgb 4;, aflflAK-wf :: O/Hfi {4e MAozquu/M i3 ‘4“(' Man Amy}.- (Mme)me 12A; “13 +mc my M4 m <0 / la. '22: 1%.? W 2%. '&(M #5 7me < J Mb? ; #19145] :0 ’“b?i(1ac d 0 7m {:44 M’ glen 1H2?“ ? 01/114 ([_9+ao. \L xi; 0" U (P (m b€~£lac f. “it hi; A 561 2‘4 {:46 ‘r'( {2, l“ “giro-mt w; d/ 2 t O c) a (m Lag—.4“ Co In é ' Wi '"i 7+ [M4 50! M (— e. g Cosiof ‘i' C (2, 2“ Stink/1L 45W [fwd/SM W film, 6 WW 2W “(M- d/ ‘3/21.l“ 6 o a a a rF-a’l‘eb 2. (20) Solve y(3)+6y” +y’ ~34y : 0. (Hint: 6“”.cost is asolution). 7?; awarém whim R3f6*Q2-+nw3q:.a " [6m 5’19 51;" 54% MM; M: Z ; ,9;ch Rhea-are M] a? / a): km {4/ R “ti-“A 56$”be 34 Afi' F3 6 f-z‘Z/wZ/M/ + A~3,’/---/I?“J)_ 8?” {46% M7 /¢»'w. £244, {IM/ :2. ,4 QMéoé/ {M'Rg-r6R2+Rfl3¢:[R-o2)m2r xii-+497 MM 47‘ A my 6 m (M “4.5,; M 42+; m (a w; (7/ R 2+3£+44 flaw/«Ad amiaifit ffkaém /. Biz: 61¢ w MW?) {44/ -4 W i: i— 12)“, flaw/l v.7" ld A a . Limo 0/360ng é 64 m Macy. (Lg cap-7&4 Qytjaé “,4 (-A,“ ,w' raga @éik46fl%/a 11906, m W W gag (R ~ {<4 +2)}-/R- (944)): Kismm am? (42% 0%»; fl; {MK-mi 801% @(4650 afing A» (Q (moétaé_ a; WW2me 7m 1 4,3 2" + if 3. (25) Solve y(4) m 8;] = 0. céqmémm gag/{um is qug’qrfl’éra M218) m <:> R (R272) (x’x’l-rlfl Mk0 <61"? K e {Va/a2}, *4 +416; _4.«A'1F3)). azf _é . I I “1‘11, 56 {4e Word/‘émA )I/F/rel +ca .1: €33 wflgfi “Hall; Sm 3f 4. o (30) Using the variation of parameters, solve y” - 43/ —I— 4y 2 (t + 1).e2t :- (5) Rewrite the equation as a system of two first order equa~ tions. ' fl“ Camfiénéfi'c e7mfi/W m’ KZ-QR-M : (K32); se' (46- mduéq" @ flwzwfl 4- {£622.}. ("/z “0W £0“ £4 9/MAMM AyQé-sz .451, x’fl/c'é‘iflC/ez'é rifl/gé 2F, Val/Maggi (I; ([12 éRVe _ " m; r / 2!. ’f 7 2'; M0 ’7 705w» 6,} {ll/z Hog {F/fc : c’) Cj/fi/ BEN-f cj/F/ 5:357; five? 2/ 7-2; _3 ? Emw gmxfigflLrfl[email protected]%w§ @276”ng 21/, 26 2%: 2/— M1 (LN/- m ' '3 r avg/M g; 5-; gar/gm .12 gxdkm a C? 214 1L 7 11‘ 2% 52 { b 7%”: \/C (U grin/H: c4e2 +-ELK(?F.+»{_':~1/i +/;~H{/ ‘9’ 3 0/4 545% '4 m 4 ‘- obs/J {Zea / ‘Kz:y/ X/ 7/“: 4‘//‘“ df)” ‘ 45,426" X; if 3.- ...
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SolutionsMidterm - MAT 212 Midterm Exam Name Student Id 1...

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