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Mathematics
Problem
If
y
=
y
(
x
)
y = y(x)
y
=
y
(
x
)
is the solution of the equation
e
sin
y
cos
y
d
y
d
x
+
e
sin
y
cos
x
=
cos
x
,
y
(
0
)
=
0
,
e^{\sin y} \cos y \frac{dy}{dx} + e^{\sin y} \cos x = \cos x, \quad y(0) = 0,
e
s
i
n
y
cos
y
d
x
d
y
+
e
s
i
n
y
cos
x
=
cos
x
,
y
(
0
)
=
0
,
then
1
+
y
(
π
6
)
+
3
2
y
(
π
3
)
+
1
2
y
(
π
4
)
1 + y\left(\frac{\pi}{6}\right) + \frac{\sqrt{3}}{2} y\left(\frac{\pi}{3}\right) + \frac{1}{\sqrt{2}} y\left(\frac{\pi}{4}\right)
1
+
y
(
6
π
)
+
2
3
y
(
3
π
)
+
2
1
y
(
4
π
)
is ............
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