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Other
Engineering Mathematics
Variables Separable Method I
The solution ...
Question
The solution of the differential equation
d
y
d
x
=
k
y
,
, y(0) = c is
A
x =
c
e
−
k
y
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B
x =
k
e
c
y
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C
y =
c
e
k
x
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D
y
=
c
e
−
k
x
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Solution
The correct option is
C
y =
c
e
k
x
d
y
d
x
=
k
y
,
y
(
0
)
=
c
d
y
y
=
k
d
x
Integrated both sides
log y = kx + log G
y = Ge
k
x
y(0) = C
⇒
G
=
c
y =
c
e
k
x
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0
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