: ` ` `

-

y' = f0 (x) + f1 (x)y + f2 (x)y2 + f3 (x)y3

(. . . 1- )

[g0 (x) + g1 (x)y]y' = f0 (x) + f1 (x)y + f2 (x)y2 + f3 (x)y3

(. . . 2- ). . [1] . . . . . 1- .

f1 ∈ C(a, b), f2 f3 ∈ C1 (a, b) f3 (x) ≠ 0 x ∈ [a, b], . . . 1- (. [2]) dz/dt = = z3 + (t). . . . 1- ; (. [2]). g0 g1 ∈ C1 (a, b) g1 (x) ≠ 0, g0 (x) + g1 (x)y ≠ 0, . . . 2- . . . 1- g0 (x) + g1 (x)y = 1/z.

. . . 1- 2- ,

(., ., [3]).

. : [1] Abel N. ., J. reine und angew. Math. , 1829, Bd 4, S. 309-48; [2] e ., , . ., 5 ., ., 1976; [3] . ., , 2 ., . - ., 1950.

. X. .


:

  1. . . 1 ( - ). . : . . ( ) [ .] - ., , 1977, 1152 . .








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