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2t 1 2   2t  3 dt

 t  2 dt   t  2 dt  2 dt  3  t  2  2t  ln3 t  2  .c

General integral, taking into account, that x  y  t , we will get
in a kind x  2 x   y  ln3 x  y  2  c or

x  2 y  ln3 x  y  2  C .
.
2.4. Linear Differential Equations of the First Order

Differential equation of the first order is named linear, if it
is simple equation of relatively unknown function and its
derivative ( y and y enter linearly):

y   P  yx  Q   x (2.25)

where   xP , Q   x - the set functions.
We will consider that functions   xP , Q   x continuous on
some interval  ba, , then for equation (2.25) the terms of
theorem Cauchy about existence and unique of decision are
executed.
If right part of equation (2.25)   0xQ we have linear
homogeneous equation (LHDE) of kind

 Py    yx 0 (2.26)

which is simultaneously equation with the separated variables.
Consequently, the method of solving is known in this case. It is
easily to make sure, that the common decision of linear
homogeneous equation is

  P  dxx
y  Ce (2.27)

where C - the arbitrary became.
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