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which determines the common decision in a non-obvious kind.
Such correlation is named the general integral of differential
equation of n-go order, and correlation which turns out from a
general integral at the concrete values of constant c 1,c 2,…,c n, is
named an integral part.

3.2. Differential Equations of Higher Orders Which
Assume the Decline of Order

Integration in the some type of equations of higher order is
succeeded in some special cases only. We will be limited to that
to the selection of separate types of such equations.

(n)
3.2.1. Equations of a Kind y =f(x)

Common decision of equation of a kind

(n)
y =f(x) (3.5)

we find the method of n-times integration. We multiply both
parts of him on dx and integrate, to get equation of (n-1)-th
order:
~
y (n  )1  y (n ) dx   f (x )dx   1 (x )  .c (3.6)

1

Repeating this operation, we come to equation of (n-2)-th
order:
~
~
~


y (n  )2  y (n  )1 dx  ( 1 (x )  )dxc 1   2 (x )  xc 1  c 2 . (3.7)

After n-times integration we get the common decision

y   (x ) c x n 1  c x n 2  ... c x  c , (3.8)
n 1 2 n 1 n

where с і (і=1,...,n) – are arbitrary constant, related to arbitrary
~
constant definitely ,...,cс ~ .
1 n

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