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Byju's Answer
Standard XII
Mathematics
Formation of a Differential Equation from a General Solution
y=acos x +bsi...
Question
y
=
a
cos
x
+
b
sin
x
is the solution of which of the differential equation.
A
d
2
y
d
x
2
+
y
=
0
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B
d
2
y
d
x
2
−
y
=
0
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C
d
y
d
x
+
y
=
0
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D
d
y
d
x
+
x
d
y
d
x
=
0
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Solution
The correct option is
A
d
2
y
d
x
2
+
y
=
0
y
=
a
c
o
s
x
+
b
s
i
n
x
⟹
d
y
d
x
=
−
a
s
i
n
x
+
b
c
o
s
x
⟹
d
2
y
d
x
2
=
−
a
c
o
s
x
−
b
s
i
n
x
⟹
d
2
y
d
x
2
=
−
y
⟹
d
2
y
d
x
2
+
y
=
0
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