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240-2006&2007-1-M10-November2006

240-2006&2007-1-M10-November2006 - Kuwait...

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Unformatted text preview: Kuwait University Math. 240 November 7, 2006 Dept. of Math. & Comp. Sc. First Midterm Exam Duration 90 Minutes Calculators and mobile phones are not allowed Answer the following questions 1. (5 points) Find the general solution of the equatiOn y"(2e‘I + in y) (13$ + (as — 3y sin y) dy : O. 2. (5 points) Solve the initial value problem saw +z3y : mm); 11(1):; 3. (5 points) Find the general solution of the equation .ry’ : y (1 + ytanx). 4. (5 points) Find the orthogonal trajectories of the family of curves 1:2 i y2 = (.353. 5. (a) (2 points) Perform the multiplication (D+$)(ID+1); D(-)=£-:E(-.) (b) (3 points) Show that the functions 3:, $2, 3521mm“ are linearly independent on (O, 00) . OO 99 bolanon Mar/4; - Z40 — ”FEW (I) 1/11/2006 9 3<1éfi+¥hdj>df+(X—3‘jS‘AnaDAjzu _ j ~r 4‘1” Aa/ao gg' (25. +1443) 41% +<><3~35”:fi) ’5 FY3193): Q , :53” 7510’) + X35 0/;(5 can: Cu) 01% X3CXJB+ijj-; (may) a; —; Sfabw) c103): x 0.1x *3ma) Li [email protected] '2 :90: ‘3’: > c: ;=> x «zeoscmv—I ® 3) X3"; 50+Efflmx) “i=6 #5} Bayjqz Q t+;Z:——;G:Kj c:g @ F: egg”: K j (”E—’yflfi’ jnkmx I’H’0657x2+c 41+ 331+ zxax‘ :o DEL ZXBCJIX + (sz_ x2) Olljzo 9”. ('ko ,_ _.._ - }* _.___. - 2X J— @_ rD/‘f d_ 2. ___v W: e .. a"; H mg a) —" 3" 9 '- zxariclx+(‘3flxlaflz)5€y:/O til?— XLjpl.+3j: K a $143551: Kg 316 ADE)— Con 56 Sch/{alga HE or 856’) ’5“) (DHNWM) : 3+ XDL'TFB’TXLDAFX ¢XDL-fi-<1"YXL)D+X C7); 59 1 ?( xL X LHK W‘; \ 2x 2%]?!er 0 2 3+2»; CD = ><(’62<+4>\1nx.—4><Lnx,z><) ’ C37<lr+lelnx-—2X1lnx)r« X #0 X” KL/ X1 j’7/Y are )Hfllrb’j final? 'emf/é??* 0Y1 C0100). @23 (mm 99 ...
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