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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 initialvalue 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] (xly)2.<217cl(2J1ylJr2 —l)d =0
y Elix3 +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:? ElAk '_u3.
iéLdC
=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)Jzi_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 =  9515" L ...
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 Spring '11
 sadik
 Differential Equations, Equations

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