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Mathematics
Mathematics
Problem
If
sin
(
y
x
)
=
log
e
∣
x
∣
+
α
2
\sin\left(\frac{y}{x}\right) = \log_e |x| + \frac{\alpha}{2}
sin
(
x
y
)
=
lo
g
e
∣
x
∣
+
2
α
is the solution of the differential equation
x
cos
(
y
x
)
d
y
d
x
=
y
cos
(
y
x
)
+
x
x \cos\left(\frac{y}{x}\right) \frac{dy}{dx} = y \cos\left(\frac{y}{x}\right) + x
x
cos
(
x
y
)
d
x
d
y
=
y
cos
(
x
y
)
+
x
and
y
(
1
)
=
π
3
y(1) = \frac{\pi}{3}
y
(
1
)
=
3
π
, then
α
2
\alpha^2
α
2
is equal to
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