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EAMCET Engineering 2005 Solved Paper
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© examsnet.com
Question : 160
Total: 160
If
d
y
d
x
=
y
+
x
tan
y
x
x
, then
s
i
n
y
x
is equal to
c
x
2
c
x
c
x
3
c
x
4
Validate
Solution:
Given that
d
y
d
x
=
y
+
x
tan
y
x
x
. . . (i)
This is a homogeneous differential equation.
Put
y
=
v
x
and
d
y
d
x
=
v
+
x
d
v
d
x
From Eq. (i),
v
+
x
d
v
d
x
=
v
x
+
x
tan
(
v
x
x
)
x
⇒
x
d
v
d
x
=
v
+
tan
v
−
v
⇒
cot
v
d
v
=
d
x
x
On integrating both sides, we get
log
s
i
n
v
=
log
x
+
log
c
⇒
s
i
n
v
=
x
c
⇒
s
i
n
y
x
=
x
c
© examsnet.com
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