5
>K)
6 p
October 15, 2009
()
October 15, 2009
1 / 27
5
5>K)
dx
= A(t)x + f (t).
dt
x(a) = x(b).
>^
X>^Lx(a) + N x(b) = 0
a, b I, L, N n n~
"
>Kk)=k"
>Kk)'^
()
October 15, 2009
2 / 27
>K)
|NH'>Kk)'^
(
4
g5|(NH)(
October 9, 2009
()
October 9, 2009
1 / 20
SN
dx
= A(t)x + f (t)
dt
(N H )
!)'K
(I) ) ( n"
(II) A) '~ Ccfw_ "
()
October 9, 2009
2 / 20
g5|)5
)'5
(1.) g 5 |NH') A 'g 5 | LH
')Eg5|')"
(2.) g
1 5
October 15, 2009
()
October 15, 2009
1 / 16
1
S|
dx1 = a (t)x + + a (t)x + f (t)
11
1
1n
n
1
dt
dx
n
= an1 (t)x1 + + ann (t)xn + fn (t)
dt
a
ij , fi , i
= 1, , n
mI '"P
dx
1
x1
dt
. dx .
x =
pAa.
pk0(Riccati)
4.2
4.3
September 30, 2009
()
September 30, 2009
1 / 14
4.2
pAa.
a.I F (x, y ) = 0.
e)y = f (x)ng.
K/
(n)
(n)
x = (t),
ry
(n1)
y (n) = (t).
^ tv :
dy (n1) = y (n) dx = (t) (t)dt
y (
4
September 29, 2009
()
September 29, 2009
1 / 12
4
4.1
F (x, y, y ) = 0
(1)
(1)
(1)
x = (t),
xy
y = (t),
<t<
(2)
(2)
(t)
F [(t), (t),
(2)
()
(t)
]=0
<t<
(1)
September 29, 2009
2 / 12
4
x
y
:
(I) y
3
AK(5
September 24, 2009
()
September 24, 2009
1/9
CO
3.1
y
dy
a.I. dx = x + f (xy).
zxf (xy)dx = xdy + ydx = d(xy).
-u = xyu du = xf (u).
dx
y
dy
~3.1-1 A dx + x + 4x y + 1 = 0.
Ay = 21x tg(x + C )C
2
Y.')cfw_
September 22, 2009
()
September 22, 2009
1 / 25
2.6
Tf
M (x, y )dx + N (x, y )dy = 0
(1)
TXtQU (x, y)&
dU (x, y ) = M (x, y )dx + N (x, y )dy.
U (x, y )
U (x, y )
= M (x, y ),
= N (x, y ).
2
September 17, 2009
()
September 17, 2009
1 / 20
2.1
dy
= h(x)g (y )
dx
(2.1)
h(x), g (x)
:
x
()
h(x)
y
g (y )
September 17, 2009
2 / 20
2.1
dy
= 3x2 y .
dx
2.1
(i)
(ii)
y=0
1
dy = 3x2 dx.
y
: n|y |