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Mathematics
Problem
If
y
=
y
(
x
)
y = y(x)
y
=
y
(
x
)
,
(
1
+
sin
(
x
+
y
)
)
d
y
d
x
=
(
sin
(
x
+
y
2
)
−
cos
(
x
+
y
2
)
)
2
(1 + \sin(x + y)) \frac{dy}{dx} = \left( \sin\left(\frac{x+y}{2}\right) - \cos\left(\frac{x+y}{2}\right) \right)^2
(
1
+
sin
(
x
+
y
))
d
x
d
y
=
(
sin
(
2
x
+
y
)
−
cos
(
2
x
+
y
)
)
2
and number of solution(s) of the equation
y
(
x
)
=
x
y(x) = x
y
(
x
)
=
x
in
x
∈
[
0
,
2
π
]
x \in [0, 2\pi]
x
∈
[
0
,
2
π
]
is 3, then value of
y
(
0
)
y(0)
y
(
0
)
is
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