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1 3
3 (x  c )
3
3  3y  x  c 2 , y  2 .
2 18

From an initial condition у(1)=1 we find с 2:

1  1 (  c ) 3 / 18 , c  3 18  . 1
2 2

Consequently, the sought decision after part is determined
by a formula
1
y  ( x 3 18  ) 1 3 . 
18

Exercises:

1. To check or the indicated functions are the upshots of
differential equations :
1 2 1
а) y  x  x ; y  y  x .
8 16
б ) y  C e 1 C x ; yy    'y 2 .
2
2. Find decision of equation:
2
d y 2
а)  y , б) xy  1 x .
dx 2
ln 'y
2
в) xy  1 x , г) xy  ' y .
x

60