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Mathematics
Mathematics
Problem
Which of the following functions
y
=
y
(
x
)
y=y(x)
y
=
y
(
x
)
satisfies the differential equation
d
y
d
x
=
2
x
y
\dfrac{dy}{dx}=2x\,y
d
x
d
y
=
2
x
y
for all real numbers
x
x
x
? (Here
C
C
C
denotes a non-zero constant.) a)
y
=
C
e
2
x
y=Ce^{2x}
y
=
C
e
2
x
b)
y
=
C
e
−
x
2
y=Ce^{-x^{2}}
y
=
C
e
−
x
2
c)
y
=
C
e
x
2
y=Ce^{x^{2}}
y
=
C
e
x
2
d)
y
=
C
e
x
2
/
2
y=Ce^{x^{2}/2}
y
=
C
e
x
2
/2
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