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Unformatted text preview: 1.(8 points) Find the general solution of the following differential equation: 3;”) — 4g“) + 4y“ — 16y” _—. 0 “‘d“mh‘w’t ism’L: Q
m4 (m...4_\ *4”). (h “dale
wi‘ {wimp} Q,“ “Q 2Q 2.(10 points) Solve the following Initial Value Problem: y= E. W) =0, y’(1) =0. 3.(8 points) Use the method of undetermined coefﬁcients to ﬁnd the general
solution of the nonhomogeneous differential equation: y” + 3y' + 23; = 83 L
h‘ *3“* 2— '29 =7 (MJerQ‘Mﬁ =0 418 points) Find the general solution of the following differential equation: my“) _ ym = 0 x+iéﬁﬂ Kant.“ : Q m(m"ﬁ(M—L)Chn—“6‘) —~n(rn—I\ (In—Zn : Q
QO—tMmo.) (On.3).— q —.. o h" (“HumQ 0" ~ﬂ 1:: “'1 H
\‘leh:\}m51Lqml—;ﬂ 5.(6 points) Let y1 = Sin 3x be a solution of the differential equation
1;" + 9y 2 {I Find a second linearly independent solution 342 for the differential equation
using reduction of order. '82 '22“ ﬁrian
I .
‘3: —_ u {punsx + 7aMCT‘q‘h‘5K
u H  ‘ '
L3; __ u ‘émsk arouseg 5); +5“ Cogs 3x —°\U‘§ih3x one = *4" EM“ * 6L“ We“ “monk H
32“" ai‘hL ‘5'— ca Hug ‘ a _ . .
lhstcém Poissx °\ D\\‘\hgx «yakhgx :_ Q l .
dcgj‘hsk +€"‘I 0*?» ex = Q 1"“ “4:141 6.(10 points) A 4foot spring measures _8__feet long after a mass weighing 8
lbs is attached tab—it. The Elaium through which the weight moves offers a '
resistance numerically equal to \/§ times the instantaneous velocity. Find the
equation of motion if the weight is released from the mullibriumposition with
a downward velocity of 5 ft/s. Find the time at which the weight attains its
extreme diaplaoeiﬁent frome equilibrium position. Does the weight passes
the equilibrium position, if it does, ﬁnd the ﬁrst time it passes through it. ®:«' 1 W :8 1F=ﬁ
5:L+ _
b=a “Na3......l %' KL
3L_; 7.(3 points) Let y1 = 32" and y2 be two linearly independent solutions of a.
secondorder differential equation such that W(yhy = —4. Find yg. ...
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 Spring '11
 sadik
 Differential Equations, Equations

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