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 We will write down equation in a kind
dy  7 x 3 y 7
 . A condition (2.20) is obviously executed.
dx 3 x 7 y 3
 7  3  7  ,0
Deciding the system of equations  obsessed
 3  7  3  ,0
  ux  ,1 dx  du ,
  , 1   0. We shall do replacement 
 y  ,v dy  dv .
dv  u 7  v 3
Obsessed homogeneous equation  . We will do
du u 3  v 7
u dv dt
replacement t  , from where v  tu,  u  t , and
v du du
dt  7  t 3
get equation with the separated variables u  t  .
du 3  t 7
We will separate variables and let us integrate:
3  t 7 du 3  t 7 du
dt  ,  dt   ,
2
2
7 t   1 u 7 t   1 u

3 t 1 1 2
ln  ln t  1  ln u  ln C
14 t 1 2
3
u  v  u  7
2
putting t  , obsessed    C v  u 2 . Now we will
v  v  u 
  xu  ,1
put  and write down the sought general integral
 v  y
after
3
  xy  1 7 2 2
   C y   x 1  . 


 y  x  1 
.
We will consider the case of equation of kind also

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