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sol_midv1f10

# sol_midv1f10 - MAT2384-Ordinary differential Equations and...

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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: MIL—— 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: (633142 — 3x2y3 + 2y)da: + (9393/ ~ 4333312 + 4m)dy = 0, y(1) = 1. W W H N «SGILHW Hy : 1m 31 - 0! x25 3&7. , NX u )X’XC; _. ’Zkij 21—9 ‘, MOT Exad“ fly—Nx; ._69<E3+3>(Z5!2~Q ._ ‘- ’ ‘— 2 g (a) H --t4(-6'Xy+3><231_1) <9 m&.W-h*Mg fat/ML; ftp/2: e, 1 e. 2. 7. “‘J/Hpég Hu~ 0DE LufH. 7'. 3 MN WaZ-wsa *Wa) 4- = o H” KM 1:, anx‘ 31w :Now taxed” H*-; 187(52— sz‘d?+‘«g ) ”x ‘ “(7‘3 <7 (9 Y A . ,BP- *EEIM“ 79F: 4x231... Hx3‘7~rl«><7+ L‘U)" 4: 7) , 2 3 t12f K. K .. 39 PL><PD=3><17~X7+ *7 “P MAT 2384 C Midterm Exam, October 22, 2010 2. [4 points] Solve the Initial Value Problem: 2 y’ — 51/ = 29:3, 31(1) = 0- 539th m in ex meim mam ODE Luca ,ngcix—cC, ~ ‘ I“? X a 3 .— SRLZ QxéXf'C'; X“—[2.SXAX+C3 ‘: _. l/XL Li L XLKXL-fc‘) : X+CK MAT 2384 C Midterm Exam, October 22, 2010 3. [4 points] Give the general solution for each of the following ODES: (1) y” —6y’+9y = 0 (2) y”—4y'+5y=0 aoémlwm 0) TL. oluomlem‘slx ‘c. Whm e3 >‘L-'€>'T‘Cl:-o :> ©I3)Z:OT:J>'>\I:>\L:3 “WI— 1 A «I ' _H’>\ 13:0 ":5 L2) 1%» omwewm WW w A + ‘1 J 9’ ' _ é ~r IbaLl(\)(3)g Ll," _L‘ 2 ({1— k 2 2+,& 0““ .. a '2 Pg. empew MWMW />\L:' ‘2"; 2* ~ \(U): C e2 0.99ka Claw/Ml MAT 2384 C Midterm Exam, October 22, 2010 4. [5 points] Solve the Initial Value Problem: 11:23!” + my’ + 9y 2 0, a: > 0, y(1) = 1, 1/0): 3 %h‘m m 4:3 OK EMQé/\_COMQ/L\I EMU“ Wk‘H’) as] 13-; C( m OM’WKLWShL WJVGK .3 MAT 2384 C Midterm Exam, October 22, 2010 5. [4 points] Give the general solution for the following ODE: MAT 2384 C Midterm Exam, October 22, 2010 6. [6 points] Use the ﬁxed point iteration method to ﬁnd the root Of 9:4 — 7g; + 3 = 0 in the interval [0,1] to 4 decimal places. Use x0 = 0.45 and make sure that the conditions for convergence of the iteration sequence are satisﬁed. XLQMA; o @> X: “‘7’: 3 N Cm}? W 0“; 6(kx): LL25. 3 V3 M ? A5 1 <\ we. lfl‘bdl 2 iii" Mg, 3 % m [0“] ? 2 ﬂ cmvwaﬂmh— \CMW 4M} 4L... IMHOM WCL w a OHﬂH-r2-©,93(((1 1X0- 0%)” 129/78: 8LX°)— t)- ...
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sol_midv1f10 - MAT2384-Ordinary differential Equations and...

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