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d y 2y<br />
5<br />
. − = ( x + 1)<br />
2 .<br />
dx<br />
x + 1<br />
dy<br />
2y<br />
dy<br />
2dx<br />
: − = 0 , =<br />
dx<br />
x + 1 y x + 1<br />
ln y = 2ln x + 1 + ln C , y = C( x +1)<br />
. y = u ( x)<br />
⋅(<br />
x<br />
2<br />
y′ = u′⋅(<br />
x + 1) + 2u<br />
⋅(<br />
x + 1)<br />
<br />
<br />
<br />
1<br />
2<br />
+ 1)<br />
u′ = ( x +1)<br />
2 3<br />
u = ( x + 1)<br />
2<br />
+ C<br />
3<br />
3<br />
2 ⎡ 2<br />
= ( x + 1) ( x + 1) + C<br />
⎢⎣ 3<br />
y<br />
2<br />
2<br />
,<br />
⎤<br />
⎥⎦<br />
<br />
2