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direction of the field in this point of the set differential equation.
It can represent this field of directions, drawing in the
proper points the segments, which form corners with an axis Ox

  arctg y (y  f (x , y )) (fig. 1.2).
Obviously, let as find points with identical numerical values
of this function can in the region of existence of function.
Geometrical place of such points is named isoclines given
differential equation. Equation of isoclines can be written down
in a kind
f ( , )x y  C  const .
Isoclines it is possible to use for approximated construction
of integral curves.
Example 1.1 To build the integral curves of differential
equation approximately
2
' y  x  y 2
.
 Isoclines in this case there is family of concentric circles
2
2
C  x  y of radius with r  C a centre in beginning of
coordinates (fig.1.3). It must draw integral curves so that in
every point a curve had direction of the field. 

1.3 Solving of Some Equations of the First Order,
Untied in Relation to Derivative

Tasks of solving of differential equations, generally
speaking, it is enough difficult. At first, their upshots exist not
always, secondly, even if exist, not always them it is possible it
is enough simple to find. We will stop to that on solving of only
some equations of the first order, untied in relation to derivative

' y  f ( , )x y (1.7)

at the special types of function f (x .y ) . By the way, equation
(1.7) can be written down in other form:
dy  ( x, y ) dx (1.8)
f

M ( x, y ) dx  N( x, y ) dy , (1.9)
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