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Byju's Answer
Standard XII
Mathematics
Properties Derived from Trigonometric Identities
Show that the...
Question
Show that the function y = A cos x + B sin x is a solution of the differential equation
d
2
y
d
x
2
+
y
=
0
.
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Solution
We have,
y
=
A
cos
x
+
B
sin
x
...(1)
Differentiating both sides of equation (1) with respect to
x
, we get
d
y
d
x
=
-
A
sin
x
+
B
cos
x
...(2)
Differentiating both sides of equation (2) with respect to
x
, we get
d
2
y
d
x
2
=
-
A
cos
x
-
B
sin
x
⇒
d
2
y
d
x
2
=
-
A
cos
x
+
B
sin
x
⇒
d
2
y
d
x
2
=
-
y
Using equation
1
⇒
d
2
y
d
x
2
+
y
=
0
Hence, the given function is the solution to the given differential equation.
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