1 . . 1.1 . ......4 1.2 ......................6
2 . . . 2.1 - ..................9 2.2 .............................................................12
3
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, , , (). ( ). , , , , .
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() n y (x), (a, b) {\displaystyle y'(x),y''(x),...,y^{(n)}(x)} n . .
() , ;
(1)
y=y(x) {\displaystyle y=y(x)} , x. {\displaystyle x,} {\displaystyle x.} {\displaystyle n} n . .
, . , , . .
, . . :
(2),
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1 . , () .
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y = y(x) F(x, y, y ')=0, y(x0)= y0, ( ).
y(x0) = y0 .
y = y(x) ( ) 1 , .
, Φ(x,y) = C, .
, Φ(x,y) = 0, .
1- , , , :
:
M (x, y)d x + N (x, y)d y = 0.
y = y (x), x = x (y).
:
x ≠ 0
, y (x)
x ≠ 0 C.