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Mathematics
Problem
Let
y
=
y
(
x
)
y = y(x)
y
=
y
(
x
)
be the solution of the differential equation
d
y
d
x
=
4
y
3
+
2
y
x
2
3
x
y
2
+
x
3
\frac{dy}{dx} = \frac{4y^3 + 2yx^2}{3xy^2 + x^3}
d
x
d
y
=
3
x
y
2
+
x
3
4
y
3
+
2
y
x
2
,
y
(
1
)
=
1
y(1) = 1
y
(
1
)
=
1
. If for some
n
∈
N
n \in \mathbb{N}
n
∈
N
,
y
(
2
)
∈
[
n
−
1
,
n
)
y(2) \in [n-1, n)
y
(
2
)
∈
[
n
−
1
,
n
)
, then
n
n
n
is equal to ______ [JEE MAINS - ONLINE - 2022]
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