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  P  dxx  P  dxx
y  e ( Q  ex dx  C ) .


It is the same formula (2.30), to which came earlier a
method Lagrange.

Example 2.10 To find the common decision of equation
y x   3y  x 2 .
3
 We will write down equation in a kind y   y  . x
x

We will enter substitution y  uv , y  u v  v u  and put
y and y in given LNDE:
3uv
u v  v u    , x
x
 3 v 
u v  u v     x . (*)
 x 
3v
3
Farther we will untie LHDE  v   , 0 obsessed v  x
x
dx
3
and put this function in (*): u x  x or du  , from where
x 2
1
u    C . Now we will write down the common decision of
x
 1  3 2
3
the given Equation: y  x   C  or y  Cx  x .
 x 

Note 2.3 If known two upshots parts y and y LNDE first
1 2
order, his common decision is written down without squares in a
kind y  C y  y  y
1 2 1
.

Example 2.11 To find the common decision of equation
2xy  y 3 dy  dx  0.

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