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Mathematics
Mathematics
Problem
Let
y
=
y
(
x
)
y = y(x)
y
=
y
(
x
)
be the solution curve of the differential equation
x
(
x
2
+
e
x
)
d
y
+
(
e
x
(
x
−
2
)
y
−
x
3
)
d
x
=
0
x(x^2 + e^x)dy + (e^x(x-2)y - x^3)dx = 0
x
(
x
2
+
e
x
)
d
y
+
(
e
x
(
x
−
2
)
y
−
x
3
)
d
x
=
0
,
x
>
0
x > 0
x
>
0
, passing through the point
(
1
,
0
)
(1, 0)
(
1
,
0
)
. Then
y
(
2
)
y(2)
y
(
2
)
is equal to : (a)
4
4
−
e
2
\frac{4}{4-e^2}
4
−
e
2
4
(b)
2
2
+
e
2
\frac{2}{2+e^2}
2
+
e
2
2
(c)
2
2
−
e
2
\frac{2}{2-e^2}
2
−
e
2
2
(d)
4
4
+
e
2
\frac{4}{4+e^2}
4
+
e
2
4
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