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Mathematics
Mathematics
Problem
Let
y
=
y
(
x
)
y = y(x)
y
=
y
(
x
)
be the solution of the differential equation
sin
x
d
y
d
x
+
y
cos
x
=
4
x
\sin x \frac{dy}{dx} + y \cos x = 4x
sin
x
d
x
d
y
+
y
cos
x
=
4
x
,
x
∈
(
0
,
π
)
x \in (0, \pi)
x
∈
(
0
,
π
)
. If
y
(
π
2
)
=
0
y\left(\frac{\pi}{2}\right) = 0
y
(
2
π
)
=
0
, then
y
(
π
6
)
y\left(\frac{\pi}{6}\right)
y
(
6
π
)
is equal to : [JEE-MAIN-2018] (1)
4
9
3
π
2
\frac{4}{9\sqrt{3}}\pi^2
9
3
4
π
2
(2)
−
8
9
3
π
2
\frac{-8}{9\sqrt{3}}\pi^2
9
3
−
8
π
2
(3)
−
8
9
π
2
-\frac{8}{9}\pi^2
−
9
8
π
2
(4)
−
4
9
π
2
-\frac{4}{9}\pi^2
−
9
4
π
2
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