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Standard XII
Mathematics
Order of a Differential Equation
Question
The differential equation representing the family of curves
y
2
=
2
c
(
x
+
√
c
)
, where
c
>
0
, is a parameter, is of order and degree as follows:
order 1, degree 1
order 1, degree 2
order 1, degree 3
order 2, degree 2
A
order 1, degree 2
B
order 1, degree 1
C
order 2, degree 2
D
order 1, degree 3
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Solution
Verified by Toppr
Given,
y
2
=
2
c
(
x
+
√
c
)
...(1)
2
y
y
′
=
2
c
.1
⇒
y
y
′
=
c
...(2)
⇒
y
2
=
2
y
y
′
(
x
+
√
y
y
′
)
On putting value of
c
from (2) in (1)
⇒
y
2
−
2
y
y
′
x
=
(
2
y
y
′
√
y
y
′
)
squaring both sides, we get
[
y
(
y
−
2
y
′
x
)
]
2
=
4
y
2
y
′
2
y
y
′
y
2
(
y
−
2
y
′
x
)
2
=
4
y
3
y
′
3
On simplifying, we get
(
y
−
2
x
y
′
)
2
=
4
y
y
′
3
...(3)
Hence, equation
3
is of order
1
and degree
3
.
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