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n
P ( )x  C  C x C x 2   C x  0
n 0 1 2 n
P ' ( )x  C  2C x   nC x n 1  0
n 1 2 n
P '' ( )x  2C  3 2C x   ( n n  1)C x n 2  0
n 2 3 n
P ( )n ( )x  ! n C  .
0
n n
.
0
From the last equation of this system C  . Then from
n
next to last equality we find that C  0. Farther „going up"
n 1
we find C n 2  0 , , C  .
0
0

4.3 Linear Homogeneous Differential Equations

For construction of common decision LHDE it is needed is
deep to learn the question of linear dependence of decisions
parts of these equations To that end we will enter notion of so
called Wronskian.

4.3.1. Wronski-Determinante

,
Definition 4.6 If functions y y , , y (n-1) are one time
1 2 n
differentiated on an interval( , )a b is named Wronski-
Determinante or Wronskian
y y y
1 2  n
'
y ' y  y '
  W ( )x  1 2 n . (4.6)
 
y 1 (n 1) y 2 ( n 1)  y (n 1)
n

In particular, at n=2
y y
1 2


.   W ( )x   y y  y y , (4.7)
2 1
1
2
y 1  y 2 

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