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Standard XII
Mathematics
Formation of a Differential Equation from a General Solution
Obtain the di...
Question
Obtain the differential equation representing the family of parabola having vertex at origin and axis along the positive direction of x-axis.
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Solution
Equation of parabola having vertex at origin and axis along the positive direction of
x
-axis is
y
2
=
4
a
x
Differentiating both sides w.r.t
x
we get
2
y
d
y
d
x
=
4
a
⇒
a
=
y
y
2
d
y
d
x
Substituting for
a
in
y
2
=
4
a
x
we get
y
2
=
4
(
y
y
2
d
y
d
x
)
x
⇒
y
=
2
x
d
y
d
x
⇒
2
x
d
y
d
x
−
y
=
0
is the required differential equation
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