, , .
, , . : (8.1) . . (8.1) z(x): , .. z(x) 1- . , . z(x) , , y. y(x)=0. , , .
.
. M(x,y)dx+N(x,y)dy=0 (9.1) U(x,y), . du(x,y)=0, , u(x,y)=c.
, xdy+ydx=0 , d(xy)=0. xy=c.
. , M N D y x. , , (9.1) , , (9.2).
. . (9.2). , u(x,y), .
, , (9.3), - . (9.3) y: . , , . ., , , .
.
M(x,y)dx + N(x,y)dy = 0 = (x,y),
(Mdx + Ndy) = 0 , . . (Mdx + Ndy)du, (x,y) . , , = 1.
, .
x y, .
, 1- : (10.1). , = (ω), ω x y, (10.1) ( ) ω: (10.2), , . . ω.
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(10.2), , = 1. M(x,y)dx + N(x,y)dy = 0 , x (ω = x) y (ω = y), : , , .
10. II- ( -). () 2- : , (2.1)
, , , , . , a0(x) ≠ 0, (2.1) , , : (2.2)
, (2.2) , , , , . , (2.2) , (2.2) . 2- .
. , .
. , (2.3) .
. (2.3) , :
.
: .
(2.3), , .
1. , (2.3), . 2. , , . . .
11. . . . II- .
n - y 1(x), y 2(x), , yn (x) n .