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MTH 205-Solution-Test-01-A-SU09

# MTH 205-Solution-Test-01-A-SU09 - American University of...

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Unformatted text preview: American University of Shariah Department of Mathematics and Statistics Test I--- A Name: K63 ID #: WITH—205, June 24—2009 Section: it for each right step. Show all your work. There will be a partial cred ' I equation. Express your solution in explicit form [20 pts] 1. Solve the foliowing differentla 5—11 =—1 + cosz(x+ y) I 2.Solve the following initial-value problem. Express your solution in explicit form [20 pts] dy xEr—+(x+l)y=e“ln(x), y(l)=0 :2) ’4. I+-.L —- C- 22"”) HJC 0% x (l+-i-)di~ x J” an: + x J- Ium=e : e w exexzxex -x ’xcx 0' (1233 :— 6’ x2“)4c[2—+c [x X a we; : ‘1': .w T...) 3633 *— grim" ’1 +C HA —- K + C; 3.Show that the following differential equation is exact then solve it. Express your solution in implicit form [20 pts] (x-l-y)2.<217c-l-(2J1y-l-Jr2 —l)d =0 y Eli-x3 +2’a “3 *‘H‘ﬂ 4. Solve the following homogenous differential equation. Express your solution in expiicit form [20 pts] :) ulxaéa __‘763alu :0 UL 3:3 1 glaze 1:? El-Ak '_u3. iéLd-C =7 QITCL‘ 3 x i I 5. Find the current in a series RL circuit with R=10 ohms and L=5 henrys, if the applied voltage varies with time according to 5 Et = U {0 volts Assume :‘(O)=0. [20 pts] Osrslsec {>1 volts { Hint: the differential equation that governed the problem is L g + Ri = EU) } 6.(Bonus Problem) Solve the following differential equation [10 points] (5x+3ey)dx +2xe"dy = 0 M [1:133 ﬂare‘jﬁgaLze‘jgﬁ 0’3 clx. 17.51% :23; (9X+3LL)Jz-i_2xdu _.Q “J, erlji 34 "-g1 —7 m4- clu 3 _ -9 =? anti?“ *7: 3 k. 3 J/Z’XA 3/39”: ﬂax/b 312', gum : e :2» :e :: x 0‘(x [Aw ‘2: “ix 97% 3 .— jzu .. __,_?-' 35—— ‘TL 2’, r 2, 5 )4. 3 5/ jig/Lu :_ x a. >7; «3/ UL .2: r x +cx & X37» -3/ UR) —_, 1; + C75 L -3/ (2‘3 = - 95-1-5" L ...
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