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Mathematics
Problem
Let
y
(
x
)
=
cos
(
3
cos
−
1
x
)
y(x) = \cos(3 \cos^{-1} x)
y
(
x
)
=
cos
(
3
cos
−
1
x
)
,
x
∈
[
−
1
,
1
]
x \in [-1, 1]
x
∈
[
−
1
,
1
]
,
x
≠
±
3
2
x \neq \pm \frac{\sqrt{3}}{2}
x
=
±
2
3
. Then
1
y
(
x
)
{
(
x
2
−
1
)
d
2
y
(
x
)
d
x
2
+
x
d
y
(
x
)
d
x
}
\frac{1}{y(x)}\left\{(x^2 - 1)\frac{d^2 y(x)}{dx^2} + x\frac{dy(x)}{dx}\right\}
y
(
x
)
1
{
(
x
2
−
1
)
d
x
2
d
2
y
(
x
)
+
x
d
x
d
y
(
x
)
}
equals [JEE(Advanced) 2014]
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