= f (x, y, y, y,
y () =
y () =
= , , () =
:
(, , , , )
f
(3.6)
:
= f I (x, )
() = y I 0 (i= 1, 2, , n) (3.9)
, , :
a x + a i = (1, 2, , )
bi + bi
(3.9) :
① (x, ) i= (1, 2, , n) │ │ M
② (1 n)
│ (x, y, │
3. , .
1- (1.7). :
= 1()
:
y=
, :
y() =
y= +
f(x)=y :
= f (x, y)
:
y () =
4. :
5. , :
1- :
= f ()
z = y = x z
x =
, ϕ (x, y) k
4 (tx, ty) = ϕ (x, y)
, x y .
:
M (x, y) dx + N (x, y) dy = 0
M (x, y) N (x, y) (x, y) ,
()
x = x -
y = y -
= 0
, :
(2.3) :
)
) = ϕ (
:
x + y + = 0 -
x + y + = 0
= c
= k
(2.3) : f (
z = , .
6. .:
7. .
8. , .:
, M (x, y) dx + N(x, y) dy = 0 (2.8)
, , (2,8) :
|
|
d U = ϻM dx + ϻN dy
ϻ ϻ(x, y) , (x, y)
:
(2.11)
(2.11) (2.10)
ϻ x, y, ,
: , ϻ (x) => - x =>
Ln M =
M= C * (2.12)
c=1, 1
x (2.12)
9. . -.:
- :
+ (x) + + (x) * + (x) y= ϕ (x) (3.1)
ϕ (x)≡0
, y y
a
+ (x) + + (x) y + (x) y = 0 (3.2)
=-