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Mathematics
Problem
Consider the differential equation
d
y
d
x
=
x
e
y
\dfrac{dy}{dx}=x e^{y}
d
x
d
y
=
x
e
y
. Which of the following gives the explicit general solution
y
(
x
)
y(x)
y
(
x
)
? a)
y
=
−
ln
(
x
2
2
+
C
)
y = -\ln\!\left(\dfrac{x^{2}}{2}+C\right)
y
=
−
ln
(
2
x
2
+
C
)
b)
y
=
−
ln
(
−
x
2
2
+
C
)
y = -\ln\!\left(-\dfrac{x^{2}}{2}+C\right)
y
=
−
ln
(
−
2
x
2
+
C
)
c)
y
=
ln
(
−
x
2
2
+
C
)
y = \ln\!\left(-\dfrac{x^{2}}{2}+C\right)
y
=
ln
(
−
2
x
2
+
C
)
d)
y
=
ln
(
x
2
2
+
C
)
y = \ln\!\left(\dfrac{x^{2}}{2}+C\right)
y
=
ln
(
2
x
2
+
C
)
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