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General integral, taking into account, that, we will get in a
2
kind x   C
x  y
tg 1
2
.
2) Lets sin t 1  . 0

Then sint   , 1 t    2 k , k  . Z As x  y  t , so we
2

get x  y    2 k , k  . Z 
2

Exercises:

1. To define the order of differential equations :
5
3
2
0
)a y 3 sin ''y  xy '  ; )б x y  3x y ' y 2  0.
2. To check or the functions indicated below are the upshots
of the proper differential equations :
2
a
'
)а y  2 (a x  ) k ( k і a - constants ) ; equation yy  ;
)б y  Ce  2x (C - constant ) ; ' 2y  y  4x equation .
3. To check or written expressions are the general integrals
of differential equation :
2x  y
2
2
2
)a x  xy  y  9 C ; equation 'y  ;
x  2y
x
2
2
)б x  y  4 C 2 ; equation 'y   .
y
4. To find differential equation, the common decision of
which the crooked are, set by equations:
) a y  Cxe x ;
C
) б y  C x  2 .
1
x

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