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y
y   0.
x
We lower his order by replacement y  p , y  p.
Obsessed :
dp p
  0 ,
dy x
dp dx
  0 ,
p x

ln p  ln x  ln C ,

p  Cx ,

from where, taking into account replacement, we reach :
 dy   C 2 
  Cx  dy  Cxdx   y  x  C 1  ,

 dx   2 
that is
C

2
y  C x  C , C  1 .
2 1 2
2
Consequently, the common decision of the set equation is
2
3
y  x  C x  C .
2 1
On the basis of theorem 6 it is possible to do a conclusion
that for finding of general decision LHDE (4.2) it is enough to
find his fundamental system of decisions and write down
general decision in a kind (4.12). 

Exercises:

1. To make LHDE after the set of fundamental system
of his decisions :
;
а) 1 ; cos x б) x e x .
;
2. To find the common decision LHDE, knowing him
one decision :

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