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Joint Entrance Examination
Mathematics
Differential Equations
Question 302
Question 302 of 490
Medium
MCQ
If
d
y
d
x
+
y
tan
x
=
sin
2
x
\dfrac{dy}{dx}+y\tan x=\sin2x
d
x
d
y
+
y
tan
x
=
sin
2
x
,
y
(
0
)
=
1
y(0)=1
y
(
0
)
=
1
, then
y
(
π
)
y(\pi)
y
(
π
)
equals:
A
1
B
-1
C
-5
D
5
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Official solution
I.F.
=
sec
x
=\sec x
=
sec
x
.
y
sec
x
=
−
2
cos
x
+
c
y\sec x = -2\cos x+c
y
sec
x
=
−
2
cos
x
+
c
; using
(
0
,
1
)
(0,1)
(
0
,
1
)
:
c
=
3
c=3
c
=
3
. At
x
=
π
x=\pi
x
=
π
:
y
(
−
1
)
=
−
2
(
−
1
)
+
3
=
5
⟹
y
=
−
5
y(-1)=-2(-1)+3=5 \implies y=-5
y
(
−
1
)
=
−
2
(
−
1
)
+
3
=
5
⟹
y
=
−
5
.
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