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Mathematics
Problem
The family of functions
y
=
C
e
3
x
y = Ce^{3x}
y
=
C
e
3
x
, where
C
C
C
is an arbitrary constant, is given. Which of the following first-order differential equations is satisfied by every member of this family? a)
d
y
d
x
−
3
=
0
\dfrac{dy}{dx}-3=0
d
x
d
y
−
3
=
0
b)
d
y
d
x
−
3
y
=
0
\dfrac{dy}{dx}-3y=0
d
x
d
y
−
3
y
=
0
c)
d
y
d
x
+
3
y
=
0
\dfrac{dy}{dx}+3y=0
d
x
d
y
+
3
y
=
0
d)
d
y
d
x
−
3
x
y
=
0
\dfrac{dy}{dx}-3xy=0
d
x
d
y
−
3
x
y
=
0
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