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Byju's Answer
Standard XI
Mathematics
Solving Linear Differential Equations of First Order
The solution ...
Question
The solution of
d
v
d
t
+
k
m
v
=
−
g
is
A
v
=
c
e
−
k
m
t
−
m
g
k
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B
v
=
c
−
m
g
k
e
−
k
m
t
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C
v
e
−
k
m
t
=
c
−
m
g
k
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D
v
e
k
m
t
=
c
−
m
g
k
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Solution
The correct option is
A
v
=
c
e
−
k
m
t
−
m
g
k
d
v
d
t
+
k
m
v
=
−
g
Integrating factor (I.F.) =
e
∫
k
m
d
t
=
k
e
m
t
∴
v
k
e
m
t
=
−
∫
g
e
k
t
m
+
c
v
k
e
m
t
=
−
g
m
k
k
e
m
t
+
c
v
=
C
.
−
k
e
m
t
−
m
g
k
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0
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