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form the differential equation of y ae3xcos x b wh
Question:
Form the differential equation of
y
=
a
e
3
x
cos
(
x
+
b
)
Where
y
′
=
d
y
d
x
and
y
n
=
d
2
y
d
x
2
?
MHT CET
Updated On:
Jun 23, 2024
(A)
y
′
′
−
6
y
′
+
10
y
=
0
(B)
y
′
′
−
6
y
′
−
10
y
=
0
(C)
y
′
′
+
6
y
′
−
10
y
=
0
(D)
y
′
′
+
6
y
′
+
10
y
=
0
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The Correct Option is
C
Solution and Explanation
Explanation:
Given,
y
=
a
e
3
x
cos
(
x
+
b
)
There are two constants a and b so differentiate two times Differentiating wr.t
x
,We get,
y
′
=
3
a
e
3
x
cos
(
x
+
b
)
−
a
e
3
x
sin
(
x
+
b
)
⇒
y
′
=
3
y
−
a
e
3
x
sin
(
x
+
b
)
⇒
a
e
3
x
sin
(
x
+
b
)
=
3
y
−
y
′
Differentiating again w.r.t
x
,We get,
3
a
e
3
x
sin
(
x
+
b
)
+
a
e
3
x
cos
(
x
+
b
)
=
3
y
′
−
y
′
′
⇒
3
(
3
y
−
y
′
)
+
y
−
3
y
′
−
y
n
=
0
⇒
9
y
−
3
y
′
+
y
−
3
y
′
−
y
n
=
0
⇒
y
′
′
+
6
y
′
−
10
y
=
0
Hence, the correct option is (C).
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