# mid2384v2 - MAT2384 Ordinary differential Equations and...

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Unformatted text preview: MAT2384 Ordinary differential Equations and Numerical Methods MIDTERM EXAM (Fall, 2009) Professor: Joseph Khoury Duration: 80 minutes (a , Last Name: First Name: Student Number: (1) This is a closed book exam. (2) Only basic calculators are allowed. Graphing or programmable calculators are not allowed. (3) The test has 6 questions worth a total of 30 points. (4) The Test has 9 pages. (5) Please write your answers in a complete and clear way. You may use the back of’the pages if you miss space. (6) You must answer all the questions. (7) Good Luck! MAT 2384 Midterm Exam, October 23 1. [6 points] Solve the Initial Value Problem: (2x312 — 3y sin m)dw + (9 (308:1: + 4\$2y)dy : 0, y(0) = 1. W W M N (Skghm 9L1: fog_3m‘mx J E 2 _ciwx+gxy Nem— txad— 7 x 341.2m AMI 44M -2~gz><1~isw>: -22. .1 (cm) “I bx '=- : 1 Vtzxx/WSS-{nx} \/ H 2X7 -37MX ﬂ ‘MVZ ~J%C3)4a 9 v 1 Th. “3wa Fewer w MY): ca -_ L —_ c, :7. ODE by '71" (xxx/LL 3‘73.%X‘)Ax + (C? YZCc91>><+ QX'Lyg) e17; : O W/ W M“ N" / ‘ 3 I. “5“”— ?xygﬂyzs'm 5N”: .—C?72&'w>< “3W 86m“- by “‘ J by. ‘ 7’!“ F ._ ’ Wang QE. 7. K] waif. (“1% a. Fumah'mx FCny) «ruck ML Lg; _ M ()7 ‘3 15—f- : Qx‘y". 3734/16X ‘f—‘b szzxyy.»3‘751’»X)Jx + ax —— XL)”; S‘ygcmx- + My) MAT 2384 Midterm Exam, October 23 2. [3 points] Solve the Initial Value Problem: y’— <2)y=x, y(1):1. SC ‘ _ ._ Z— gyg’w’kw L0 (N CW5? - 69(4524... mach ODE L’J‘H‘ “ J r( X) “1 X . (SM "39mm- 56’, .(‘(><')<:‘x -r C fﬂ‘ >9<1>< (a 7H):- L -— ,= l. ijX)Ax:5~2§-¢lx: -—2—\V\|X‘: \/V\( L) __D Q, X’L 3‘ AK“? C leL +L) 7”): FT“ XL Z—UM‘+C) CDLZ‘ MAT 2384 Midterm Exam, October 23 3. [4 points] Solve the Initial Value Problem: x211” +xy’ +93; 2 0, a; > 0, y(1) = 1, y/(1)= _2 Sﬁuklﬁx QM thﬂx CA1\) 5161‘ LC,( 1% U/meﬂxcsrC/u‘skc ‘Wh'm L; N622? (ck-U “RTE”:- 0 (\m + :C) 17% m:i34'_ \/ (x) v: C‘ ‘fQLS\!V\('\$\4/\X') MAT 2384 Midterm Exam, October 23 4. [6 points] Give the general solution for each of the following ODES: (1) y” —4y’+8y = 0 (2) y” + 63/ +9y : 0 gaggle“ gym CM’XAC/l'E/L’L‘SKC— {Aer-wok CM»; Ali—L4 A+ 7 .1 3 thl Ie~-V(x) __ Q: .2.C .— w— I Q «4) >X‘JL.‘ 2. Z Z. . X , x (gxma/VQQ. (3)674 CaDQDx)+ CLQ anllz-X) \2) m (Cl/vow c/l—ou‘slw'c by ,‘v MAT 2384 Midterm Exam, October 23 5. [5 points] Give the general solution for the following ODE: ym — 3y/ + 2y 2 0. Sea/J4 stx TM, dado um, kM‘sls‘L EW‘LSK 9—, >\$43> +2.20 ,_ 87 9‘:\ an»; ml (3%)} Aiﬁﬁﬂ—z (ex—x) mixx) -; (A-~\)L’>\~\)U+Z) 2 ©~0Z©+U MAT 2384 Midterm Exam, October 23 6. [6 points] Use the ﬁxed point iteration method to ﬁnd the root of x3 — 5x + 2 = 0 in the interval [0,1] to 4 decimal places. Use :30 : 0.4 and make sure that the conditions for convergence of the iteration sequence are satisﬁed. ugw— 5AX+ 2. 3 ,. ~ 3 L ' ‘ 3L ’ 9"*’3X+Z=OC=> X= M: \$019300: *2» Also/afﬁx»; 7) Dné lvcn Ck m4 {Cal-3 42 kc”; ck gums s2, [0,6, . 9 p q 1 g “Mt-9&4, %‘(X‘): 13.5; 4/) («MHMW (ha/A. l3‘(x)l (’2 r--y <~l , )— U“ 0) l3= ':&Q.h‘oy ,u f). I r, » ‘ i a \ _ o I by?) UML" ‘9'; 7‘0 e 2 :l 73 X0“; 0 ‘1 :43 Ml; :1 O z .Xizgmc') _ owqu +7. _ 0mm 3’ . ,3 , Mg: wu- «MW rt multh 5” 3 “w- an» owl!” , aqua 5, ...
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## This note was uploaded on 02/24/2010 for the course SITE MAT2384 taught by Professor Josephkhoury during the Fall '09 term at University of Ottawa.

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mid2384v2 - MAT2384 Ordinary differential Equations and...

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