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Mathematics
Problem
The family
y
=
C
1
cos
x
+
C
2
sin
x
y = C_{1}\cos x + C_{2}\sin x
y
=
C
1
cos
x
+
C
2
sin
x
, with independent constants
C
1
C_{1}
C
1
and
C
2
C_{2}
C
2
, is given. What is the lowest-order differential equation whose solution set consists exactly of this family? a)
y
′
′
−
y
=
0
y'' - y = 0
y
′′
−
y
=
0
b)
y
′
+
y
=
0
y' + y = 0
y
′
+
y
=
0
c)
y
′
′
+
y
=
0
y'' + y = 0
y
′′
+
y
=
0
d)
y
′
′
+
2
y
=
0
y'' + 2y = 0
y
′′
+
2
y
=
0
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