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some function  yxu ,  which we will find after a formula (2.9).
It is thus possible to lay down x  ; 0 y  1:
0 0
x y  0  x
u   3x 2 y  ln y dx    0  3   cos dyy   x 3 y  x ln y 0 
0 1  y 
y 3
 sin y  x y  x ln y sin y sin . 1
1

We will write down a general integral in a kind (2.10), will
carry a constant size sin 1 immediately in right part and add to
arbitrary constant:
x 3 y  x ln y  sin y  . C

In practice it is possible to come to the answer yet quick, by
an artificial way. It is enough to expose handles, then to unite
members of equation so that in every group it was possible to
see the complete differential of some known function and,
finally, all groups to unite under a general integral. In the
example considered already it takes place so:
 x 
3x 2 ydx  x 3 dy    ln ydx  dy dy  cos ydy  , 0


 y 
d   dyx 3  ln yx  d sin y  0 ,
d (x 3 y  x ln y sin y )  . 0

From here general integral x 3 y  x ln y  sin y  . C 

2.2 Method of Integrating Cofactor

If Equation of kind P  , yx dx  Q  , yx dy  0 is not
equation in complete differentials, it is possible to make to
attempt to pick up a so called integrating cofactor     yx, ,
that is function as a result of increase on which both parts of

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