if y=(1+x/1-x)2 prove that (1+x2)dy/dx=4y.
Answers
Answered by
0
Step-by-step explanation:
y=
1+x
1−x
y=
(1+x)(1−x)
(1−x)(1−x)
y=
1−x
2
1−x
−(1)
⇒
dx
dy
=
(
1−x
2
)
2
1−x
2
dx
d
(1−x)−(1−x)
dx
d
(
1−x
2
)
⇒
dx
dy
=
1−x
2
−
1−x
2
+(1−x).
1−x
2
x
⇒(1−x
2
)
dx
dy
=
1−x
2
−1+x
2
+x−x
2
⇒(1−x
2
)
dx
dy
=
1−x
2
−1+x
⇒(1−x
2
)
dx
dy
=−(
1−x
2
1−x
)
From (1)
(1−x
2
)
dx
dy
=−y
(1−x
2
)
dx
dy
+y=0
Similar questions