sol_midv2f10

# 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~>()+/)[email protected] 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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sol_midv2f10 - MAT2384—Ordinary differential Equations...

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