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AIEEE 2005 Math Solved Paper
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© examsnet.com
Question : 44
Total: 71
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 2
order 1 , degree 1
order 1 , degree 3
order 2 , degree 2
Validate
Solution:
y
2
=
2
c
(
x
+
√
c
)
.....(1)
2
y
y
′
=
2
c
.1
or
y
y
′
=
c
....(2)
⇒
y
2
=
2
y
y
′
(
x
+
√
y
y
′
)
[ On putting value of
c
from
(
i
i
)
in
(
i
)
]
On simplifying, we get
(
y
−
2
x
y
′
)
2
=
4
y
y
′
3
Hence equation (iii) is of order 1 and degree 3 .
© examsnet.com
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