1. F(x, y, y')=0, ; ; ' , .
', : y' = f(x,y) , .
: , ( ): P(x,y)dx+Q(x,y)dy =0, (, ) Q (, ) .
, , .. .
2. =j(), .
.
, , , .
( ). f (x, ) f'y (x, ) G , (0; 0) G, y'=f(x, ), : = =0.
. , , .
, (x0; 0) G . , G .
, =j() 0 0, .
, , . .
, (0; 0) .
, , , .
3. G =j(, ), , , , (0; 0)Î G, =0 , =j (, 0) j (0, )=0.
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4. G =j (, 0), =(, ) =0.
, , , ( 0; 0).
, - .
. y'=f(x, ) =j () - . , . , ' (; ) f(x, ). , y' = f(x, ) (; ) ' . , (; ). (; ) , f (, ). , .
, y'=f(x, ) , , .
, .