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JEE Main Math Class 12 Differential Equations Part 1 Questions
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Question : 3
Total: 100
The difference between degree and order of a differential equation that represents the family of curves given by
y
2
=
a
(
x
+
√
a
2
)
,
a
>
0
is ......... .
[26 Feb 2021 Shift 1]
Your Answer:
Validate
Solution:
Given,
y
2
=
a
[
x
+
√
a
2
]
,
a
>
0
...(i)
Differentiating both sides w.r.t. '
x
',
2
y
d
y
d
x
=
a
[
1
+
0
]
=
a
. . . (ii)
Use Eq. (ii) in Eq. (i) to eliminate the constant '
a
'.
y
2
=
2
y
d
y
d
x
(
x
+
√
2
y
√
d
y
d
x
)
y
2
−
2
x
y
d
y
d
x
=
2
√
2
⋅
y
√
y
⋅
d
y
d
x
√
d
y
d
x
Squaring on both sides,
y
4
+
4
x
2
y
2
(
d
y
d
x
)
2
−
4
x
y
3
d
y
d
x
=
8
y
3
(
d
y
d
x
)
3
Thus, degree of above differential equation is 3 and its order is 1 .
Difference between degree and order
=
3
−
1
=
2
© examsnet.com
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