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. y  u     xvx (2.32)


Then y  u v  v u  and substitution y and y in LNDE

results of equation vu  v u   P  uvx  Q   x .
We will rewrite the last equality in a kind


vu  u v   P    Qvx    x (2.33)

As for determination the two so far unknown functions   xu
and   xv we have one correlation (2.32) only, we can choose
one of these functions at own discretion, namely will find
v   x 0 so that  Pv    vx 0.
Then, as it considered higher,   xv is the decision of proper
LHDE and can be written down after a formula (1.42), which
we will lay down in C  1:

  P  dxx
v  e (2.34)

We will put   xv in (2.33) and for determination of the
second unknown function   xu get equation with the separated
variables:
  P  dxx
u e  Q  x ,
or
 P  dxx
du  e Q  dxx .

As a result of integration we get a function

u   Q  ex  P  dxx dx  C . (2.35)

Pursuant to (2.32) we write down the common decision
LNDE in a kind:

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