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)'^
(1) > ^ x(a) = x(b)"
g
i(t)LH')
uNH')L
t
x(t) = (t) C +
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 = (x, y )
(II) x = (y, y )
x
y
:
(III) F (x, y ) = 0
(I
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 ?~"
22
2
()
September 24, 2009
2/9
CO
3.1
dy
a.II. dx
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 ).
x
y
U (x, y ) C C
)
()
?~"
September 22, 2009
2 / 25
2
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 | = x3 + C1 ,
C1
y = 0,
y = Cex
C=0
3
C = eC1 = 0
(i)
3
y
7
5'
)cfw_
October 15, 2009
()
October 15, 2009
1 / 15
'C
7.1
S
dn x
dn1 x
+ a1 (t) n1 + + an (t)x = 0
dtn
dt
(1)
cfw_(1)A'g'A)"
|^4)"
.Eulerz~X"
()
October 15, 2009
2 / 15
cfw_
GIe(1)')x = (t)uvC
x = (t)yn 1"
(i.) - x = (t)y u z
(t)
dn y
dn1 y
+ b1 (t) n