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Mathematics
Mathematics
Problem
If
y
=
y
(
x
)
y = y(x)
y
=
y
(
x
)
is the solution of the differential equation,
e
y
(
d
y
d
x
−
1
)
=
e
x
e^y \left( \frac{dy}{dx} - 1 \right) = e^x
e
y
(
d
x
d
y
−
1
)
=
e
x
such that
y
(
0
)
=
0
y(0) = 0
y
(
0
)
=
0
, then
y
(
1
)
y(1)
y
(
1
)
is equal to: (1)
2
+
log
e
2
2 + \log_e 2
2
+
lo
g
e
2
(2)
2
e
2e
2
e
(3)
log
e
2
\log_e 2
lo
g
e
2
(4)
1
+
log
e
2
1 + \log_e 2
1
+
lo
g
e
2
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