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KEAM 2016 Math Paper
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© examsnet.com
Question : 118
Total: 120
The differential equation representing the family of curves
y
2
=
a
(
a
x
+
b
)
where a and b are arbitrary constants, is of
order 1, degree 1
order 1, degree 3
order 2, degree 3
order1, degree 4
order 2, degree 1
Validate
Solution:
We have,
y
2
=
a
(
a
x
+
b
)
⇒
y
2
=
a
2
x
+
a
b
On differentiating w.r.t.
x
, we get
2
y
d
y
d
x
=
a
2
⇒
y
d
y
d
x
=
a
2
2
⇒
y
⋅
d
2
y
d
x
2
+
d
y
d
x
⋅
d
y
d
x
=
0
y
⋅
y
2
+
(
y
,
)
2
=
0
Hence. order and degree of the given equation is 2 and
1
,
respectively.
© examsnet.com
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