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Question
Mathematics
The solution of dy=cosx(2 - y c o s e c x)dx, where y=√2 when x=π / 4 , is
Q. The solution of
d
y
=
cos
x
(
2
−
y
cosec
x
)
d
x
,
where
y
=
2
when
x
=
π
/4
, is
1516
201
NTA Abhyas
NTA Abhyas 2020
Differential Equations
Report Error
A
y
=
s
in
x
+
2
1
cosec
x
20%
B
y
=
t
an
(
x
/2
)
+
co
t
(
x
/2
)
20%
C
y
=
(
1/
2
)
sec
(
x
/2
)
+
2
cos
(
x
/2
)
30%
D
None of the above
30%
Solution:
Given,
d
x
d
y
=
2
cos
x
−
ycos
x
cosec
x
⇒
d
x
d
y
+
yco
t
x
=
2
cos
x
∴
I
F
=
e
∫
co
t
x
d
x
=
e
l
n
(
s
in
x
)
=
s
in
x
∴
Solution is
ys
in
x
=
∫
2
cos
x
s
in
x
d
x
+
c
⇒
ys
in
x
=
∫
s
in
2
x
d
x
+
c
⇒
ys
in
x
=
2
−
cos
2
x
+
c
At
x
=
4
π
,
y
=
2
∴
2
s
in
4
π
=
2
−
cos
2
(
π
/4
)
+
c
⇒
c
=
1
∴
ys
in
x
=
−
2
1
cos
2
x
+
1
⇒
y
=
−
2
1
.
s
in
x
cos
2
x
+
cosec
x
⇒
y
=
−
2
s
in
x
1
(
1
−
2
(
s
in
)
2
x
)
+
cosec
x
⇒
y
=
2
1
cosec
x
+
s
in
x