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Tugas 6 kalkulus lanjut
Heri Risdianto
Tugas 6
MATA KULIAH:
“KALKULUS LANJUT”
DOSEN PENGAMPU
Prof.Dr.P. Siagian, M.Pd
NAMA: HERI RISDIANTONIM : 8106172005
PENDIDIKAN MATEMATIKAPASCA SARJANA
UNIVERSITAS NEGERI MEDAN2010
Tugas 6 kalkulus lanjut
Heri Risdianto
Selesaikanlah dengan metode deret kuasa
1. y’ – 2y = 0
2. y’ – ½ y = 0
3. y’’ + y = 0
Penyelesaian
1. y’ – 2y = 0
020 0
1
m m
mm
mm xaxma
0...)22222(...)54320( 44
33
2210
45
34
2321 xaxaxaxaaxaxaxaxaa
0...)25()24()23()22()2( 445
334
2231201 xaaxaaxaaxaaaa
0303
23
23
0202
02
12
12
0101
3
4)2(23
23
023
242
)2(22
22
022
202
aaaa
aa
aa
aaaa
aa
aa
aa
aaaa
0505
45
45
0404
34
34
15
4)
3
2(25
25
02512
8)
3
4(24
24
024
aaaa
aa
aa
aaaa
aa
aa
...55
44
33
2210 xaxaxaxaxaay
...15
4
12
8
3
422 5
04
03
02
000 xaxaxaxaxaay
xe
xxxxxay
2
...)15
4
12
8
3
4221( 5432
0
xeay 20 .
Tugas 6 kalkulus lanjut
Heri Risdianto
2. y’ – ½ y = 0
02
1
0 0
1
m m
mm
mm xaxma
0...)2
1
2
1
2
1
2
1
2
1(...)54320( 4
43
32
2104
53
42
321 xaxaxaxaaxaxaxaxaa
0...)2
15()
2
14()
2
13()
2
12()
2
1( 4
453
342
231201 xaaxaaxaaxaaaa
0303
23
23
0202
02
12
12
0101
48
1)
8
1(
2
13
2
13
02
13
8
1
4
12
)2
1(
2
12
2
12
02
12
2
10
2
1
aaaa
aa
aa
aaaa
aa
aa
aa
aaaa
0505
45
45
0404
34
34
3840
1)
384
1(
2
15
2
15
02
15
384
1)
48
1(
2
14
2
14
02
14
aaaa
aa
aa
aaaa
aa
aa
...55
44
33
2210 xaxaxaxaxaay
...3840
4
384
1
48
1
8
1
2
1 50
40
30
2000 xaxaxaxaxaay
x
e
xxxxxay
2
1
...)3840
1
384
1
48
1
8
1
2
11( 5432
0
xeay 2
1
0 .
Tugas 6 kalkulus lanjut
Heri Risdianto
3. y’’ + y = 0
0)1(0 0
2
m m
mm
mm xaxamm
0...)(...)4230201262( 55
44
33
2210
57
46
35
2432 xaxaxaxaxaaxaxaxaxaxaa
0...)42()30()20()12()6()2( 557
446
335
2241302 xaaxaaxaaxaaxaaaa
0606
46
46
46
0404
24
24
24
0202
720
1)
24
1(
30
130
1
30
03024
1)
2
1(
12
112
1
12
0122
102
aaaa
aa
aa
aa
aaaa
aa
aa
aa
aaaa
0617
57
57
57
1515
35
35
35
1313
13
5040
1)
120
1(
42
142
1
42
042120
1)
6
1(
20
120
1
20
0206
16
06
aaaa
aa
aa
aa
aaaa
aa
aa
aa
aaaa
aa
...77
66
55
44
33
2210 xaxaxaxaxaxaxaay
...5040
1
720
1
120
1
24
1
6
1
2
1 760
51
40
31
2010 xxaxaxaxaxaxaay
...5040
1
120
1
6
1
720
1
24
1
2
1 71
51
311
60
40
200 xaxaxaxaxaxaxaay
xx
xxxxaxxxay
sin
7531
cos
6420 )
5040
1
120
1
6
1(...)
720
1
24
1
2
11(
xaxay sin.cos. 10
