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Unformatted text preview: Text" 2. S's/whats
Math 533 5‘ Pk) Problem 1. Consider the differential equation my”+ky’+cy=Fsin(wt) _.. Q (a) Find the particular solution of this problem.
If 5?: A Stkwi? + Emsw‘t _ . K ‘ ‘91P": +Auoowi7  Fav’gmwt W”: “$3?
$0 0 beam» ,MUALHP +C—JkiK5P’: CgMw’) (ALb‘iwtfBaJuiJ . . +l< (Awasat— Busﬂwt) ‘
:L‘. <A(G‘MWL)+M '~ BK“) ) Svkwl" + (B (C‘MWL) +Akw) “5‘4“.“
. :=' \Fsmwtﬂ ' Ami??? (b) Under what conditions on m, k and c do we have real, distinct roots for the
characteristic equation ? KLalmw )0 I
l ( c) Under what conditions do we have resonance in this problem ? Raow bum5 MW
69' sea) as ch“ PJ‘UEVBM‘ o r 5) Problem 3. Find the general solution to the problems : (a) 16 Y”(X) + 24 Y’(X) f 9 Y(X) — 0 . "Id—5:9 .39 \6}.+2.q.)+?=o ____/_.___
‘52 T
)3 "i2: = ”if; (M44321 mt) ‘ 10 W) (b) y +=2y+5y Sinxcosx.
I N )1. , ‘ «f .. M o .I .. ..
Jaguar“ Mm ﬁll/LET?“ (4,,»th
(LnLa 12.3.;ka55 $42,; = 2.9:“; aux, w. WHITE Hg; SAL an. 2 947mg;
' . 2... =3 5,: Asdzz + 64052:; /’"/’( RX ﬁx
.5p :2 AS'WI 21L +8605 9? , jp’: 1490327; “Raﬁ Stilt— \ 3‘," : "LfASMlK “‘ LE5 CM 9.9. , \\ _. ll , __ sun.
9 5‘4—23 +59... 2—1_ SW 4 . . I ‘
3(1): t. (clash. +¢,_ sum + J Smlsc. "‘13: 00529:. 3’1‘ 14 ...
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 Fall '08
 DAMON

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