第二章 二階與高階的線性微分方程 式ind.ntou.edu.tw/~b0170/math/94-1/ch02...
Transcript of 第二章 二階與高階的線性微分方程 式ind.ntou.edu.tw/~b0170/math/94-1/ch02...
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Linear Ordinary Differential
Equationn
ydegree1y
1.51.6
),()()()()()( 122
21
1
10 xbyxadxdyxa
dxydxa
dxydxa
dxydxa nnn
n
n
n
n
n
=+++++
L
6.1
5.1065
1.10
33
32
4
4
2
2
2
2
2
xxedxdyx
dxydx
dxyd
ydxdy
dxyd
dxdyxy
dxyd
=++
=++
=
+
1.1degree21.51.6
2
dxdy
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()
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()
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()
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()
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()
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()
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()
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()
yyyy
yy
21
21
21
,,
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()
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()
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)2()1(,,
)1(0
LL
LLL
xeyba
byyay
=
=++
)4(21),4(
21
,)1()3()3(0)(0)(
)1(
22
21
22
2
baabaa
baeba
eyey
x
xx
=+=
=++=++
==
LL
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:
)4(21),4(
21
22
21
baabaa =+=
04,:304,:2
04,:1
2
2
2
baba
ba
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()
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()0=++ byyay
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()
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()0=++ byyay
y1(method of reduction order) y2 (p75)
=
=
Udxyy
ey
UPdx
12
21
1
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()0=++ byyay
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())1(0 LLL=++ byyay
:
)4(21),4(
21
22
21
baabaa =+=
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()
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()
)1(0 LLL=++ byyay
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-()
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-()
025.2: 2 = yyxyx
025.30)2()15.2(
2,5.2
2
2
=+
=++
==
mmmm
ba
5.0,40)5.0)(4(
==+
mmm xx
xxy 1121
215.0
1 ====
42 xy =
4212211
1 xcx
cycycy +=+=
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-()
2/)1(1:
axyII =y1(method of reduction order) y2 (p95)
xxxyy a lnln 2/)1(12==
2/)1(21
2/)1(2
2/)1(12211
)ln(:
lna
aa
xxccy
xxcxcycycy
+=
+=+=
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2/)1(21 )ln(:
axxccy +=
043: 2 =+ yyxyx
04404)13(
4,3
2
2
=
=++
==
mmmm
ba
2,20)2)(2( == mmm
xxxyyxy lnln, 2122
1 ===
2212211 )ln( xxccycycy +=+=
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-()
)]lnsin()lncos([
,:
21
xvBxvAxy
ivumivumIII
u +=
=+=
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)]lnsin()lncos([
, 21xvBxvAxy
ivumivumu +=
=+=
0137: 2 =++ yyxyx
0136013)17(
13,7
2
2
=++
=++
==
mmmm
ba
im 2313932,1 ==
2,3 == vu
[ ])ln2sin()ln2cos(3 xBxAxy +=