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Mathematics
Problem
If a curve
y
=
y
(
x
)
y = y(x)
y
=
y
(
x
)
passes through the point
(
1
,
π
2
)
\left(1, \frac{\pi}{2}\right)
(
1
,
2
π
)
and satisfies the differential equation
(
7
x
4
cot
y
−
e
x
csc
y
)
d
x
d
y
=
x
5
,
x
≥
1
,
then at
x
=
2
,
the
(7x^4 \cot y - e^x \csc y) \frac{dx}{dy} = x^5, \quad x \ge 1, \text{ then at } x = 2, \text{ the}
(
7
x
4
cot
y
−
e
x
csc
y
)
d
y
d
x
=
x
5
,
x
≥
1
,
then at
x
=
2
,
the
value of
cos
y
\cos y
cos
y
is : [NCERT : PL-324 | April 4, 2025 (II)] (a)
2
e
2
−
e
64
\frac{2e^2 - e}{64}
64
2
e
2
−
e
(b)
2
e
2
+
e
64
\frac{2e^2 + e}{64}
64
2
e
2
+
e
(c)
2
e
2
−
e
128
\frac{2e^2 - e}{128}
128
2
e
2
−
e
(d)
2
e
2
+
e
128
\frac{2e^2 + e}{128}
128
2
e
2
+
e
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