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dx M (x , ) y
  , (1.10)
dy N (x , ) y

dx 1
.   f 1 (x , ) y . (1.11)
dy f (x , ) y

In the last record of role x and y changed: x became an
unknown function and y – independent variable. Often for
plenitude of research of decisions of equation (1.7) it is needed
to consider simultaneously and equation (1.11).

1.3.1 Equation with the Separated and Separated
Variables and Panders to Them

Equation of such kind

 dxxP  Q  dyy  0 (1.12)

it is named equation with the separated variables and had a
general integral

 P  dxx   Q  dyy  C (1.13)

where C – is the arbitrary became.
Equation of kind

   dxyQxP  P    dyyQx  0 (1.14)
1 1 2 2
or

y  f 1     yfx 2 (1.15)
are named equations with the separated variables.
Solving of such equations consists in the report of them to
the kind (1.12) by actions which will illustrate subsequent
examples. For example, dividing both parts of equation (1.14)
on a function     yQxP 0, we come to equation with the
2 1
separated variables in a kind
12