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Byju's Answer
Standard XII
Mathematics
Local Maxima
The different...
Question
The differential equation of all parabolas whose axes are parallel to
y
-axis is:
A
d
3
y
d
x
3
=
0
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B
d
2
x
d
y
2
=
0
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C
d
3
y
d
x
3
+
d
2
y
d
x
2
=
0
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D
d
2
y
d
x
2
+
2
d
y
d
x
=
0
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Solution
The correct option is
A
d
3
y
d
x
3
=
0
Equation of parabola is
(
x
−
h
)
2
=
4
a
(
y
−
k
)
Differentiating w.r.t. x, we get,
⇒
2
(
x
−
h
)
=
4
a
y
1
⇒
(
x
−
h
)
=
2
a
y
1
⇒
1
=
2
a
y
2
⇒
y
2
=
1
2
a
Differentiating w.r.t. x, we get,
⇒
y
3
=
0
⇒
d
3
y
d
x
3
=
0
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0
Similar questions
Q.
The differential equation whose general solution is given by, y =
(
c
1
c
o
s
(
x
+
c
2
)
)
−
(
c
3
e
−
x
+
c
4
)
+
(
c
5
s
i
n
x
)
, where
c
1
,
c
2
,
c
3
,
c
4
,
c
5
are arbitrary constants, is
Q.
If
y
=
(
a
x
+
b
c
x
+
d
)
, then
2
d
y
d
x
.
]
d
3
y
d
x
3
is equal to
Q.
If
m
and
n
are order and degree of the equation
(
d
2
y
d
x
2
)
5
+
4
(
d
2
y
d
x
2
)
(
d
3
y
d
x
3
)
+
(
d
3
y
d
x
3
)
=
x
2
−
1
then
(
m
,
n
)
=
Q.
The degree of the differential equation,
(
d
3
y
d
x
3
)
2
+ x
d
2
y
d
x
2
+ y = 0 is
Q.
The order and degree of
[
d
2
y
d
x
2
+
(
d
y
d
x
)
2
]
1
/
2
=
d
3
y
d
x
3
is:
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