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Mathematics
Mathematics
Problem
Let
y
=
y
(
x
)
y = y(x)
y
=
y
(
x
)
be the solution of the differential equation
d
y
d
x
=
2
(
y
+
2
sin
x
−
5
)
x
−
2
cos
x
\frac{dy}{dx} = 2(y + 2 \sin x - 5)x - 2 \cos x
d
x
d
y
=
2
(
y
+
2
sin
x
−
5
)
x
−
2
cos
x
such that,
y
(
0
)
=
7
y(0) = 7
y
(
0
)
=
7
. Then
y
(
π
)
y(\pi)
y
(
π
)
is equal to a.
2
e
π
2
+
5
2e^{\pi^2} + 5
2
e
π
2
+
5
b.
e
π
2
+
5
e^{\pi^2} + 5
e
π
2
+
5
c.
3
e
π
2
+
5
3e^{\pi^2} + 5
3
e
π
2
+
5
d.
7
e
π
2
+
5
7e^{\pi^2} + 5
7
e
π
2
+
5
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