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 dx  a x  a y  a z ;
 dt 1 2 3

 dy
  b x b y 2  b z ;
1
3
dt (7.8)

 dz
  c x  c y  c 3 . z
1
2
 dt
We will search the separate upshots of the system in a
kind:]
x   e rt , x   e rt , x  e  rt , (7.9)

where are , , ,r   - indefinite constant, which it is needed to
find.
Putting functions (7.9) in (7.8) and abbreviating on a
rt
0
cofactor e  , we will get:

 r  a   a   a  ;
2
3
1

 r  b  b   b  ;
2
3
1

 r  c  c   c  ;
3
1
2
or
 (a  ) r   a   a   0 ;
1
2
3
 b  (b  ) r   b   0 ;
 1 2 3 (7.10)

 c  c   (c  ) r   0 .
1
2
3
So the problem of interests is nontrivial decision of this
system, because at       0 get the trivial decision:
x  y  z  0. That the system of linear algebraic homogeneous
equations had nontrivial decision, it is needed, that its
determinant is zero:
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