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which we and will mainly farther examine. In particular,
equation (1.3) can be rewritten in a kind
dy
 f  yx,  or dy  f  , yx  .dx Increasing the last equality on
dx
some function  , yxQ  0 , it is possible to write down
differential equation of the first order in a kind

 , yxP dx  Q  , yx dy  0 (1.4)

which takes that advantage, that variables and here become
equal in rights, that is each of them it is possible to examine as a
function of the second.
We will make examples of differential equations of the first
order in different considered forms:
  y x y 2  1  , 0
 y  2 x , y
 x 3y dx  xydy  . 0

Finding of unknown function, that is included in differential
equation, is named his solving or integration.
Definition 1.3 Differentiated function on this interval is
named the decision of equation (1.3) on some interval  ba,  a
function y   ,x which at substitution in equation (1.3)
converts him into an identity at all x   ,ba , that is
 x   ,ba :    x  f  ,x   .x
Definition 1.4 Curve that is determined by equation
y   ,x is named an integral curve differential of equation.
The decision of differential equation can be got as in an
obvious form y   ,x so in a non-obvious kind  , x y  0 -
in this case speak that the integral of differential equation was
got. It is possible also to get the decision of differential equation
in a parametric form x   , yt    .t Differential equation,
generally speaking, is considered untied and in that case, when it
is resulted to squares that is operations of finding of indefinite
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