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Mathematics
Problem
Let
y
=
y
(
x
)
y=y(x)
y
=
y
(
x
)
be the solution of the differential equation
(
3
y
2
−
5
x
2
)
y
d
x
+
2
x
(
x
2
−
y
2
)
d
y
=
0
(3y^2-5x^2)y\,dx+2x(x^2-y^2)\,dy=0
(
3
y
2
−
5
x
2
)
y
d
x
+
2
x
(
x
2
−
y
2
)
d
y
=
0
such that
y
(
1
)
=
1
y(1)=1
y
(
1
)
=
1
. Then
∣
(
y
(
2
)
)
3
−
12
y
(
2
)
∣
\left|(y(2))^3-12y(2)\right|
(
y
(
2
)
)
3
−
12
y
(
2
)
is equal to: (1)
32
2
32\sqrt{2}
32
2
(2) 64 (3)
16
2
16\sqrt{2}
16
2
(4) 32
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