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Joint Entrance Examination
Mathematics
Differential Equations
Question 260
Question 260 of 490
Medium
MCQ
If
y
=
(
2
π
x
−
1
)
csc
x
y=\left(\dfrac{2}{\pi}x-1\right)\csc x
y
=
(
π
2
x
−
1
)
csc
x
solves
d
y
d
x
+
p
(
x
)
y
=
2
π
csc
x
\dfrac{dy}{dx}+p(x)y=\dfrac2\pi\csc x
d
x
d
y
+
p
(
x
)
y
=
π
2
csc
x
,
0
<
x
<
π
/
2
0<x<\pi/2
0
<
x
<
π
/2
, then
p
(
x
)
p(x)
p
(
x
)
equals:
A
cot
x
\cot x
cot
x
B
csc
x
\csc x
csc
x
C
sec
x
\sec x
sec
x
D
tan
x
\tan x
tan
x
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Official solution
Differentiating
y
=
(
2
π
x
−
1
)
csc
x
y=\left(\dfrac2\pi x-1\right)\csc x
y
=
(
π
2
x
−
1
)
csc
x
and comparing with the given ODE yields
p
(
x
)
=
cot
x
p(x)=\cot x
p
(
x
)
=
cot
x
.
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