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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
=
e
α
x
+
y
d
x
dy = e^{\alpha x + y}\,dx
d
y
=
e
α
x
+
y
d
x
;
α
∈
N
\alpha\in\mathbf{N}
α
∈
N
. If
y
(
log
e
2
)
=
log
e
2
y(\log_e 2)=\log_e 2
y
(
lo
g
e
2
)
=
lo
g
e
2
and
y
(
0
)
=
log
e
(
1
2
)
y(0)=\log_e\left(\frac{1}{2}\right)
y
(
0
)
=
lo
g
e
(
2
1
)
, then the value of
α
\alpha
α
is equal to ____. [JEE MAINS - ONLINE - 2021]
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