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class 12
Math
Calculus
Differential Equations
520
150
The differential equation of all circles passing through the origin and having their centres on the x-axis is
(a)
x
2
=
y
2
+
x
y
d
x
d
y
(b)
x
2
=
y
2
+
3
x
y
d
x
d
y
(c)
y
2
=
x
2
+
2
x
y
d
x
d
y
(d)
y
2
=
x
2
−
2
x
y
d
x
d
y
Correct answer:
(c)
520
150
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Similar topics
relations and functions
trigonometric functions
inverse trigonometric functions
application of derivatives
integrals
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View Similar topics ->
relations and functions
trigonometric functions
inverse trigonometric functions
application of derivatives
integrals
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Solve the differential equation
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Solve the following differential equation:
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y
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Given two curves:
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Write the sum of the order and degree of the differential equation
(
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Related Questions
Let
y
(
x
)
be a solution of the differential equation
(
1
+
e
x
)
y
p
r
i
m
e
+
y
e
x
=
1
.
If
y
(
0
)
=
2
, then which of the following statements is (are) true? (a)
y
(
−
4
)
=
0
(b)
y
(
−
2
)
=
0
(c)
y
(
x
)
has a critical point in the interval
(
−
1
,
0
)
(d)
y
(
x
)
has no critical point in the interval
(
−
1
,
0
)
From the differential equation of family of lines situated at a constant distance p from the origin.
If
y
(
x
)
satisfies the differential equation
d
x
d
y
=
x
x
2
−
2
y
where \displaystyle{y}
Let the population of rabbits surviving at a time t be governed by the differential equation
(
d
p
d
t
t
=
2
1
p
(
t
)
−
2
0
0
.
If
p
(
0
)
=
1
0
0
, then p(t) equals
Solve the differential equation
d
x
d
y
−
3
y
cot
x
=
sin
2
x
given
y
=
2
when
x
=
2
π
˙
Solve the following differential equation:
x
d
y
−
y
d
x
=
x
2
+
y
2
d
x
Given two curves:
y
=
f
(
x
)
passing through the points (0,1) and
g
(
x
)
=
∫
−
∞
x
f
(
t
)
dt passing through the point
(
0
,
n
1
)
. The tangents drawn to both the curves at the points with equal abscissas intersect on the x-axis. Find the curve
y
=
f
(
x
)
.
Write the sum of the order and degree of the differential equation
(
d
x
2
d
2
y
)
+
(
d
x
d
y
)
3
+
x
4
=
0
.
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