tugas matematika teknik kimia ii-b
TRANSCRIPT
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TUGAS MATEMATIKATEKNIK KIMIA II-B
Winindyah Ayu Larasati (2313100112)
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E!SAMAAN "I#E!ENSIAL BIASA $!"E 2
022
02'2"
2
2
=+
=+
y
dx
dyx
dx
ydx
yxyxy
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a1(%) & -2 a1(0) & -2a2(%) & 2'% a2(0) & Sehingga titik tidak ordinary. Maka,
a1%(%) & -2% a1%(0) & 0a2%2(%) & 2% a2%2(0) & 0Titik ordinary, maka titik dari ODE orde 2 iniadalah regular singular. Penyelesaianmenggunakan deret Frobenius.
0
2
2
10
1022
2
2
2
2
=
+
=
=+
yxdx
dy
dx
yd
xxy
dx
dyx
dx
ydx
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=
+
=
+
=
+
++=
+=
=
0
2
0
1
0
)1)(("
)('
n
rn
n
n
rn
n
n
rn
n
xrnrnCy
xrnCy
xCy
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0)2)1(2)1)(((])1)(([
0)2())1(2())1)(((
0)2())(2())1)(((
0)(2))((2))1)(((
1
11110
1 1
1
1
1
1
0
1
0 00
1
0 0
1
0
2
=++++
=++++
=++++
=++++
=+
=
=
+
+
=
+
=
=
++
=
+
=
=
++
=
+
k
rkkkkr
k k
rk
k
rk
k
k
rk
k
n n
rn
n
rn
nn
rn
n
n n
rn
n
rn
n
n
rn
n
xCrkCrkrkCxrrC
xCxrkCxrkrkC
xCxrnCxrnrnC
xCxrnCxxrnrnCx
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)1(
2
2)1(
)(2)1)((
0)(2)1)((
0)1)1((2)1)((
02)1(2)1)((
:RekurensiRelasi
1
00)1(
:IndicialPersamaan
1
1
1
1
1
11
2
1
+
=
=++=++
=+++=++++
=++++
==
=
rk
CC
CrkC
rkCrkrkC
rkCrkrkC
rkCrkrkC
CrkCrkrkC
r
rrr
kk
kk
kk
kk
kk
kkk
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Untu r1&0* +,&1
Maa* ada r1&0 tida daat dis./.saian
dst.
...
12
211
2
1
2
122
111
1
=
=
=
=
=
CC
CC
k
CC kk
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Untu r2&1* +,&1
....
15
4
5
2
3
2
4
2
3
4
3
2
2
2
2
21
2
2
155
12
4
133
122
111
1
dst
CC
C
C
CC
CC
CC
k
CC kk
==
==
==
==
==
=
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5432
15
4
3
2
3
422 xxxxxxy +++++=