. , , . , . , . , , , n .
n
F (x, y(x), y '(x), y ''(x), , y(n)(x)) = 0, F (n + 2)- , x (a,b), y(x) . n .
1
f(x)dx + g(y)dy = 0 f() g(y).
a(x) b(x) , [a;b] .
a(x) b(x) , [a;b] , n > 1.
M (x, y)d x + N (x, y)d y = 0 , F (x, y), .. d F (x, y) = M (x, y)d x + N (x, y)d y. F (x, y) = C . C .
n- F (x, y, y ',..., y (n)) = 0 y = y (x) n , n - .
́ ́ ́ . 1900 . . . .
, .
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