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Mathematics
Problem
Determine the general implicit solution of the differential equation
d
y
d
x
=
3
x
2
e
y
\displaystyle \frac{dy}{dx}=3x^{2}e^{y}
d
x
d
y
=
3
x
2
e
y
. Which of the following is equivalent to the general solution? a)
e
y
=
x
3
+
C
e^{y}=x^{3}+C
e
y
=
x
3
+
C
b)
e
−
y
=
−
x
3
+
C
e^{-y}=-x^{3}+C
e
−
y
=
−
x
3
+
C
c)
y
=
−
x
3
+
C
y=-x^{3}+C
y
=
−
x
3
+
C
d)
e
−
y
=
x
3
+
C
e^{-y}=x^{3}+C
e
−
y
=
x
3
+
C
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