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Byju's Answer
Standard XII
Mathematics
General Solution of a Differential Equation
Verify that ...
Question
Verify that
y
=
2
sin
3
x
is the solution of the D.E
d
2
y
d
x
2
+
9
y
=
0
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Solution
y
=
2
sin
3
x
d
y
d
x
=
6
cos
3
x
d
2
y
d
x
2
=
−
18
sin
3
x
d
2
y
d
x
2
+
9
y
=
−
18
sin
3
x
+
9
(
2
sin
3
x
)
=
−
18
sin
3
x
+
18
sin
3
x
=
0
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Similar questions
Q.
Verify that
y
=
4
s
i
n
3
x
is the solution of the differential equation
d
2
y
d
x
2
+
9
y
=
0
.
Q.
Verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.
(i)
y
=
e
x
(
a
cos
x
+
b
s
i
n
x
)
:
d
2
y
d
x
2
−
2
d
y
d
x
+
2
y
=
0
(ii)
y
=
x
sin
3
x
:
d
2
y
d
x
2
+
9
y
−
6
cos
3
x
=
0
(iii)
x
2
=
2
y
2
log
y
:
(
x
2
+
y
2
)
d
y
d
x
−
x
y
=
0
Q.
Verify that y =
a
e
−
x
is a solution of
d
2
y
d
x
2
=
1
y
(
d
y
d
x
)
2
Q.
Verify
y
=
a
e
x
is a solution of
d
2
y
d
x
2
−
y
=
0
, find particular solution when
y
(
0
)
=
1
.
Q.
y
=
4
s
i
n
3
x
is a solution of the differential equation
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