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JEE Main Math Class 12 Differential Equations Part 2 Questions
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© examsnet.com
Question : 5
Total: 124
If
y
=
y
(
x
)
is the solution of the differential equation
d
y
d
x
+
2
y
=
s
i
n
(
2
x
)
,
y
(
0
)
=
3
4
, then
y
(
π
8
)
is equal to :
[5 Apr 2024 Shift 1]
e
−
π
∕
8
e
−
π
∕
4
e
π
∕
4
e
π
∕
8
Validate
Solution:
👈: Video Solution
d
y
d
x
+
2
y
=
s
i
n
2
x
,
y
(
0
)
=
3
4
I.F
=
e
∫
2
dx
=
e
2
x
y
⋅
e
2
x
=
∫
e
2
x
s
i
n
2
x
dx
y
⋅
e
2
x
=
e
2
x
(
2
s
i
n
2
x
−
2
cos
2
x
)
4
+
4
+
C
x
=
0
,
y
=
3
4
⇒
3
4
⋅
1
=
1
(
0
−
2
)
8
+
C
3
4
=
−
1
4
+
C
1
=
C
y
=
2
s
i
n
2
x
−
2
cos
2
x
8
+
1
⋅
e
−
2
x
x
=
π
8
,
y
=
1
8
(
2
s
i
n
π
4
−
2
cos
π
4
)
+
e
−
2
(
π
8
)
y
=
0
+
e
−
π
4
© examsnet.com
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