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Question
Mathematics
If x sin ((y/x)) dy=[y sin((y/x))-x]dx and y(1) =(π/2), then the value of cos ((y/x)) is equal to
Q. If
x
s
in
(
x
y
)
d
y
=
[
ys
in
(
x
y
)
−
x
]
d
x
and
y
(
1
)
=
2
π
, then the value of cos
(
x
y
)
is equal to
3074
219
VITEEE
VITEEE 2007
Differential Equations
Report Error
A
x
B
x
1
C
l
o
g
x
D
e
x
Solution:
Given : x sin
(
x
y
)
d
y
=
[
ys
in
(
x
y
)
−
x
]
d
x
⇒
d
x
d
y
=
ys
in
(
x
y
)
ys
in
(
x
y
)
−
x
Put
x
y
=
z
⇒
d
x
d
y
=
z
.1
+
x
.
d
x
d
z
∴
x
.
d
x
d
z
+
z
=
x
s
in
z
z
x
s
in
z
x
=
zcosecz
⇒
x
d
x
d
z
=
−
cosecz
⇒
−
s
in
z
d
z
=
x
d
x
⇒
cosz
=
l
o
gx
+
c
⇒
cos
(
x
y
)
=
l
o
gx
+
c
But y
(
1
)
=
2
π
⇒
x
=
1
,
y
=
2
π
∴
cos
2
π
l
o
g
(
1
)
+
c
⇒
c
=
0
∴
cos
(
x
y
)
=
l
o
gx