240-2004&2005-3-F10-July2005

# 240-2004&2005-3-F10-July2005 - '* was?» A KUWAIT...

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Unformatted text preview: '* was?» A KUWAIT UNIVERSITY Ordinary Differential Equations Date :July 28 ,2005 Math.& Comp.Dept. Final Examination (Math-240) Duration: TWO Hours Calculators and Mobile phones are not allowed. AnSWer all of the following questions. Each questions is worth 5 points. 1. Obtain the general solutions the differential equation : (y + 2112112)dm + (2x + 3\$2y)dy = O. 2. Find the general solution of the equation : d3: — (:2: +x3y)dy =0. 3. Find the general solution of the equation using inverse differential Opera: tors : (n2 A 41) + 3)y 2 exsinz + 1133? 4. Show that y = e” is a solution of the following differential equation : my” — 2(2): + 1);,” + (I + 2)'g = 0. Find the general solution for the following 11onhomogeneous differential equation : my” — 2(93 + 1)y’ + (a: + 2)y : (:r - 2)ez. : —25 - . EtWﬂ) _ s(1—e ) 5. Find. (a) L t/8( . L 1{W . 0 6. Use the Laplace transform to solve the initial value problem : 1’”(t) — 4Y’(t) +4Y(t) : F05), s _ 0 , 0 g t < 2 rm) 2 0, Y’(O) = 3, “ he” 1" (5) _ 2320-2), t 2 2. 7. Solve the given differential equation by means of pOWer series about the point :1: = O . Find the recurrence relation and the first ﬁve non-zero terms of the series : (l +3.2)y” +:z.vg' —y :0. 8. (3.) Find the value of A, such that the curve given by the equation 3; = Cl sins: are orthogonal trajectories of the family of curves y2 = Aln [coast] +02. (b) Show that : (D — m)n (stem) 2 0, k = 0,1,2,- - -,(n s 1)‘ c State Wether the following differential equation is linear or nonlinear and write its order, (ma + W — 3y = 0. OO 99 IZXJZ) c9 ><+ (2x + :3 X3} ; a Cg . . x - r . . Cg; _ K : kit LN r )JU'LLLLI') eﬂ 01X ,__ >51: '15 >52 ‘ 3:63 j at: 2 9:33 J): “hm—hi __ _ dc _ u— I“ f xv J DU “27 __.. _ k I IA}: : ﬁg z j» 23 )4 ﬂirt E (Dal-4} D+3>j : Sn x .+ f/ L .m.,:4.m+5;o .4; (“m _g)(*m——O -; 0 _3x C: 3 Z ﬂaws—WU) h. gigs»- (\$*§Tsiyz l 58%)] Mpg? Egg Se 3*‘2 SiWL siﬁi (a . J A _ __2_'_c:'; 3 __ L 5 p_—_, .._ ._ T£>ij~1ﬁxﬂ)j+(%%U=<X<ﬂd% F —. (ix [5 & Sahjrﬁv-x 1%cr‘ r'gtm‘ifj‘iﬁkﬁa‘u:‘JJ x " J¥.ﬁx .”.ﬁ" J" ’ 3:166, ,j: '2; cw: 1.3: 2.: (“+224 eﬁ-L‘E’“ wx' \ ', . . ' 7 ' ‘ 3’. a+llfe¥+w 8:, -9106} U (fax-i- Haj + (Ki-l) 'Véixz (>02) EX / ,Y mag/13%: +7)“ -—,2Lx)fr_'__}x/zﬁ E35? U95); abﬂ‘iﬂﬁ; X~ 1) “xx «wk (x—2.) \ -‘ a . ? _7‘r _ #1:;— _ {U U) (/Uaiuf kw * 2“— 1 XML” gr r-u—‘kfl/LA X A C, — f H— L)tLU:: X‘f“ 01X: ——J-——.. 2 OFK , _ . x3 x?‘ X5 X >73 a. g U=——-§l—+X+C2X+C1 2.x X i K :_gxc+Xc+Qx¢+Q€ ;:51Hk%+%§/:,FGQ +13%) ; E 0 263—2) 52C O4t<a “1:2; 3/1029; 0 You) :5 .x‘ Ga}; g L. F ...
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## This note was uploaded on 02/23/2010 for the course DIFFRENTIA 0410244 taught by Professor Diffrential during the Spring '10 term at Kuwait University.

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240-2004&2005-3-F10-July2005 - '* was?» A KUWAIT...

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