240-2006&2007-3-M20-July2007

240-2006&2007-3-M20-July2007 - ‘ ‘Ii’uwait...

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Unformatted text preview: ‘ ‘Ii’uwait University Math 240 Date : 17 July 2007 Dept. OfMath & Comp.Sci. Second Midterm Duration : 90 minutes Calculators and mobile phones are NOT allowed . Answer all of the following questions. Each questions 5 points. 1. Find the general solution of (2x+1)y”~4(x+1)y'-l—4y=rf1 given y1 = 62x is a solution of the corresponding homogenous equation. 2. Use the inverse differential operators to solve (general solution): (4) 2 w Ir _ x y — y +2y—e cosx. 2 x ix. 8+6 3. Use the variation of parameters method to solve, y” — y = 4. Find the general solution of ym + y(5) + 431(5) + 4);“) z 0. , 5. In the following questions write TRUE or FALSE, and in each case justify your answer. (a) (D+x )(x3D—1)=(x3D—1)(D+x) . (b) The set { ex, 8—2x, 82x, sinh 2x lisa linearly independent set. Good Luck 99 PM“: 24-0 QQ R 17. 73mg; «1'- G’JWEW 4 (1+!) 9+4)» :&%;L€W ’\ . (it y -:_ Vie/17kg. yl : Cvlv+2Vj 821 3“: cv“—Wv'-—+/+v>a” ® -« 1 V” 4’ ASL: V‘: Pigs-1+) Uzi v‘——~w :9 v"-: od‘ 7/7“. ‘ +’ db”. 4% m N {TU/7+1) ) en m :31“ ' vim a; , LA: MM 61 ’Z . '-‘. r. Jn . 4: w 1 C C“2341 ’j (274,97, +9 2&1“) "’r 1 ‘(Z"+3) . - zvc—H' V: %:@-7L+l)+ Ck (1+‘)_€(27c+4) A” C2,- V:- Vfii?‘ .: _‘_ Cir 62,611 @ yW~ 2%” +27” 2, e.“ (.531 Ah\%-@- mmgwI—LM+L) t O om: OI 0) (ii V 1 4—7—7 6‘w% - . t Hum k ' Did 9—055] “”""DL’LD ~24) 4.1,) (.0552 K039 l :7 :H D r -1 - ’x .\ ,- Qiloi’Hkvxm 1 "are (461% y : yc “tyla 2 H V 6) y ’ y — Kite—4L a ‘ 9&0 ;r A 0‘) 6"»? {3(1) (3% ‘ 79 1 ,‘3‘ _‘ 1 (E7: 6 f C ._ H [1,. €5+e”7‘ \ ’ Cw} ‘FWMU . Run. A ’- 67‘+e‘7‘ A : 11-1 2‘”- W : -- Jar/{MCH‘E’ ) 5‘ - * 95" 29ch g V ' "" ’L :‘i *r éz’iattfl cm: 7t 63 f3 We” L M )Uig O. @ ‘ 97(5)_+ [51* 4y4f.‘: O W. q (mac Unqfi. w?”_+ 4W4 4) ’: O A L ‘ _ mm (van/H) Lim~+cej -0 ‘ m:0,0,010/-() iii :1 jt.’ ’3- Cl +CLX+53 XL‘E’CZfWBfiL (Ewe “7"(éw7l'f'(7 FJ‘VX @ Qoercxgor'OL/ «a x3 0‘54— :xlpw “074% o] ; 19:3 [pm—{r L x4+zczlflD D .- ‘XJ V L93 D — D (9+1): M (12‘ ‘3 ‘79 P'**’t9 i D V Cm: __ 1'7 Dmy 1’3 121.7%”) f. p Y flwm/ \ W W ,+ W L N27 ‘+ y} 997 "‘7 '7: 76,361 L/ ""F‘ C714;- CvL fag) L/ ~ 1 “Zr-7K . ~~ Lb) Em 7 E? 2 S’rb\‘€\7'1 r ' - x . W 0an a": (bun/2' (Le'rmflflwrvhm :5 “70. OO 99 ...
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240-2006&2007-3-M20-July2007 - ‘ ‘Ii’uwait...

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