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Mathematics
Mathematics
Problem
Let
y
=
y
(
x
)
y = y(x)
y
=
y
(
x
)
be the solution of the differential equation
(
x
y
−
5
x
2
1
+
x
2
)
d
x
+
(
1
+
x
2
)
d
y
=
0
(xy - 5x^2\sqrt{1+x^2})dx + (1+x^2)dy = 0
(
x
y
−
5
x
2
1
+
x
2
)
d
x
+
(
1
+
x
2
)
d
y
=
0
,
y
(
0
)
=
0
y(0)=0
y
(
0
)
=
0
. Then
y
(
3
)
y(\sqrt{3})
y
(
3
)
is equal to (a)
5
3
2
\frac{5\sqrt{3}}{2}
2
5
3
(b)
14
3
\sqrt{\frac{14}{3}}
3
14
(c)
2
2
2\sqrt{2}
2
2
(d)
15
2
\sqrt{\frac{15}{2}}
2
15
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