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 x 2  x 3

y    C 1 dx  C 2   C 1 x  C . As we integrated

2
 2  6
twice, got two arbitrary constant, which noted C and C .
1 2
Putting the set regional terms, we will form the system of
two equations for searching for of arbitrary constants:
1
 C 1 C 2  ,0
6

 4  2C C ;
 1 2
3

7
From where C   and C  1 .
1 2
6
Consequently, the partial decision of equation y '' x after
x 3 7
regional terms 1( y ) , 0 ) 2 ( y  0 has a kind: y  x  . 1
6 6
The unique partial decision is found in the considered
example, that satisfies regional terms. However so will be not
always. Can so happen, whatever differential Equation of the
second order will have partial decision after regional terms
y (x )  y , y (x )  y or will have endless their amount. The
1 1 2 2
native difference of setting of regional terms from initial
consists herein. If the set initial conditions
y (x )  y , y (x )  y Cauchy theorem guarantees put task
0 0 0 0
will have the unique decision. If the set regional terms, finding
the common decision, we will be able to set, whether the task of
upshots has and how many.
We will notice that not always the common decision of
differential equation of the n-th order succeeds to be got in a
kind (2.4). Mostly in the process of solving we get correlation of
kind

Ф(х, у, c 1,c 2,…,c n)=0,

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