sol_midv2f10 - MAT2384—Ordinary differential Equations...

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Unformatted text preview: MAT2384—Ordinary differential Equations and Numerical Methods—Fall 2010 MIDTERM EXAM (October 22, 2010) Professor: Joseph Khoury. Duration: 80 minutes Last Name: First Name: Student Number: (1) This is a closed book exam. (2) Only basic scientific calculators are allowed. Graphing or programmable cal— culators are not permitted. (3) The exam has 6 questions worth a total of 30 points. (4) The exam has 9 pages. (5) Please write your answers in a complete and clear way. You may use the back of the pages or the additional pages at the end if you need more space for your work. (6) You must answer all the questions. MAT 2384 C Midterm Exam, October 22, 2010 1. [7 points] Solve the Initial Value Problem: 3952343 — 2y — 6xy2)dx + (49:33,? — 4:10 — 9m2y)dy = 0, y(1) = —1. M H M ) L z N‘TEXCLLF m H7: qxlyz_;_)2yd) NX211XV-\1_’V’3{3 O t I. R 41% “c.1171 H..Nx__ _3xzagr7_Té,w a”; 511?, WW $39 H “ ~9c—3x‘aaum) “Sag-4‘3 “‘7 HJArpaa HM ODE ‘27 7 In /‘(\I)a. e, a. 6 -7 7‘ Z J -- <3 ' 3'3-LLX»51><\/) 7* My“ 23%— Mfih TWW Hit a 3 IL“ Exapl» - --o+ @3310” 7 P ham FLX/V) WLJVL‘QL Egg—H ) DY 149601,; £71, a W0 H nyE’glegTM‘Y) BF 3 1" 2 5o><73’=’>F(Y/7)3XY 3;: x7.“ y L 1 L1 2 March \\\C,‘1)‘~= 0 LE H33“><‘1"6\X7+ m _ >c7~ MAT 2384 C 2. [4 points] Solve the Initial Midterm Exam, October 22, 2010 Value Problem: y’—§y=2x4, y(1)=0. gyms“ TL; 40 Gk Lam {ASLW LUSH gm? ma (‘(x>—— ZXH. flu gab/dwva gig ~31~1X H X Y L‘ 3/ 2X c‘X-r C; E ZXAXfC M 5"‘>'<“G‘X C 3 1 “PS :73 ><\é‘x T C/ Y: X3 <52xéx+c>= >6 (X +Q) .1 ____________________ V)? _ =1>C=‘) - 5 3 W Y£I>=0=I> WC 0 MAT 2384 C Midterm Exam, October 22, 2010 3. [4 points] Give the general solution for each of the following ODES: (1) 3;” ~ 8y’ + 163/ = 0 (2) y” — 2y’ + 2y = 0 XQKMVW U) Tl“, omrfldem‘slw Lifmflvl'i‘ww MAT 2384 C 4. Midterm Exam, October 22, 2010 [5 points] Solve the Initial Value Problem: $274" + 901/ + 43; = 0, 93 > 0, 34(1) 2 1» 3/,(1) : 2 a; |) E"— l .. 2’ 7-“ 1 E <~==> MZ+H20C5> “\v 4’ AMI ma 94.3w = o ‘ ‘ V {194:3}: ,2 Wye” WW’36L‘Q‘L \. >( \ n \ \——.-_b C‘- 2..—-;.b 2 K ‘4‘ Vs ny): C(9:>@L~>()+/)4M@ X) (M MAT 2384 C Midterm Exam, October 22, 2010 5. [4 points] Give the general solution for the following ODE: //l y +2y”—y'—2y=0- seam m 0W.u)eu‘s}fg 6: ‘m in '3 % “~11 ’XL’ A32 :0 6;) “ALL’>\+'Z)—()\+z) I: oer.) (>\+Z-)(>5—\)=0 --=L> $1-2 )érlj agzx ; MAT 2384 C Midterm Exam, October 22, 2010 6. [6 points] Use the fixed point iteration method to find the root Of m4 — 6x + 2 = 0 in the interval [0,1] to 4 decimal places. Use m0 = 0.35 and make sure that the conditions for convergence of the iteration sequence are satisfied. % M £09: XH-éX/rz / :fi £4 Cakmwm 0%; {fine 3 >0) (EU): -3 <0. 87 fig :hmaak \meL Xq—6X+2=Q 95> ><~ Xuz- MECX)‘; X+7— 5 5 (£204.06 (9 Lo Cmi'imwv: 0“; €909: x3 4:3 03w .. ‘1 _ ‘ .3 f)" 2. ‘ . 4 <2” “X: 0.335% ate! Lt (item/e pédsba' ...
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This note was uploaded on 02/02/2011 for the course MATH MAT 2384 taught by Professor Khoury during the Spring '10 term at University of Ottawa.

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sol_midv2f10 - MAT2384—Ordinary differential Equations...

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