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  3sin x  2cos x  2C  C  2C
1 1 2
.
So such functions are the decision of the system
y  2sin x C x C  ,
1 2

z   3sin x  2cos x  2C x C  2C .
1 1 2

Note 7.1 To one equation of the n-th order can erect not
only the normal systems of equations but also systems of
equations of higher orders.

7.3 Solving of System of Linear Homogeneous Equations
With Constant Coefficients

We will write down the system of linear Equations in the
unfolded kind:

 dy 1 ( )x y  *
 dx  p 11 ( )x y  p 12 2  p 1n ( )x y  f 1 ( ) ,x
1
n

  (7.7)
 dy
 n  p n 1 ( )x y  p n 2 ( )x y   p nn ( )x y  f n * ( ) .x
1
n
2
 dx
Clearly, that the system (7.7) can be untied by the method
of report of her to one equation of the n-th order by the method
of exceptions. But, taking into account, that we will consider the
coefficients p ( )x  a  are constant and such method (we
kl kl
will name as matrix). For comfort we will be limited to the
case n  3, that is limited to three equations. We will write down
them in such denotations:

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