MA
227|: DDES
Cw
Sern
xan tt 2
20)3/2y
wwnert
-3
A
.-3
consid
-3-r
Cr+2)rty)o
2.
-lr+u) +alr+y)=o
Ageres
(3
))(3)
.))(3)> (
when
-3+2
-3+2
and
t
The
()
(-3+
cgeredor corespondg
()
()
(
Y)-G)
J)-()
-3+4
3, +
lat , I
|pog ( )
Hence, eLgenvecao
we seok
tat
slton
2t
genu
+
-4t
-()e
eotors
of
systen
esylibum soltn tor
a
stoble.
Sinh
-2t
-6e
= Ax +9(E)
Conside
Vhdetemnd ceRcint
m
uld be oP e
on
paiclarsud
the
-at
ate
be- 2t
+
a at e t a b e w2t
rt) =
Sst
Nt
nhomoses sytn
non
)ete
-2t
-24
-at
a e -aate
-2t
e
+bet))
-3
compenng colnt
3
Cof e
(-<)
te-h
- ag
-3
we see
hat
a mt
tn
he
Let
(a
can e genvelor
(g e 3
3+2
-342
(3)
t a,= a, = k
e
(k
a
ne
b
( b2
)
)
(
--()(E)
-sb, +ba
(:)-($)
-3
)
b
b
-b,tb
k+6
b -b,
k-2
)
..
kt6
-btb,
k-z --4)
bi -b,
2
kt4
k=-2
in
e cen choose vod
-b,+ b,
-2+6
4
-)b=b - 4 )
forb, thet at conreent r ino)
Let b=
b
()
(pge
hadar sohon
-at
v(t)=(-)te
()e
forxsAx)
bekre
wgot
souhan
gnerl sobtan
+(-3)te
+C.()e
C(:)e
*(.")e-at
Diagonalzon
Ax +gE)
6e2
(t
-3
O).T-()
2
make ehane
x =ly
of uanles
y'Dy +T
.26
[-6e -2t
22
- 4
-26
-3e
t
-t
\-3e
-26
(geS
+ay,
-ae
3, t 4 4 , -4e
S2dt
e
+
y,
)
ategradny
e
-
2
+(ye)- -z
ye = -at
+C,
+C,e
e
at
1,= -4e
t
26
¬) - a ttC,e
2
76)=/-at
e t C,e
o-2t +
C,e
C,e
+C, e
-2
-2t
’xe) =/ -2te+C,c
-ate
+C,e
-2t
+C,e
2t
te
Ce
()e
te
-26
A
a E) =/e
Fundmtd ma
-st
-e
- e - t a e t - e 4t
-2t
-e
e
-4t
e
-e
e
-ae
(t)
u (E)
Lt)
Ct) ucE)
dt
e
e
u (t) = (
Se
Jt
t
(
Aence
t
de
-at +C,
Co
(E)
u
pCE)
(t)=
enerel solnu x
e
-at
ae
-e
[-ate
-2t
-ate
C,e
-2t
L2t
e
+ C,e
()()cys()e
at
+
+ alat )x-) y
aa)
2
l~)
+
(c-)
pont
an
1S
ab)
Neeto
tye sene
abot
ose
osenus
S(nt)a,
nte
(b)
ntc- 2
(a
n
o
t
3
nt c
a(atctc-)an
ntC
2(ntc) Catc-) a,
ntC-|
no
no
ntc
ntc-\
a lntc) (ntc-)on
n=o
ni
ntc-|
t
(nc) an
n=0
alnt
23an
ni
nl
tote) aa
2)an-,
a(ac-)(tcc)(ntc-t) a, -
34nl
-Cnte-la,
C-I
Ca sC
+ accc-) a,
of c
cot
aclc-l+c ) an
indicil
ac(c-i) +c
equalo
c(acc-)+) =o
as
(2c-)=0
C= O
indcal
bots
C - , = w h his not
ant
s nota pos
thrtntgr,
benin
ro
two
cf
eope ct
Soluhn.
Coof
aln+c)(ntc-) (nt) )an
t
+
-alhtc-)Ca+c 2)
-Catc- ) + 3
-(ntc-)2(nte-2)+)
=0
--O
30
a)«+
+(-3a,)>
t
(
2
a)
etc
2
3)
a(
=a,a(3) -2
-3
()()
3a0
rco
)
()
n=|
O-3
etohon
when
n(an-)
an
=(n)
(an
-3)3)
when
get
lot recence
re
2c-)
(2n4 (ntc)
an
ntc-)(nt2c-3-3
nt)(ent2c
an-)
=(c-)(2n+
2c-3)
)4,
+3) -3)(ant2c
Cntc- t(- -)an
(nrc)2n
tac
n+-) (an t (3)-3)-3
)
(n+)(ent ()- )
(n-)(an-) -3
nl
(nt)(an)
/(an-) Cn-) -3
On
(3nt)n
c=
recurence relocton or
(a-00) -3
-3
ao
3
ao
(3) Ci)
(n2
3(3
s(2)
Hence a l
2
an
1
By,(o)
2
witl
whet
(i) doman ct ld
s la]<!
A8
conitns