Differential Equations Quiz
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Question 1
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Consider the IVP
y
′
′
+
y
=
cos
(
t
)
y'' + y = \cos(t)
y
′′
+
y
=
cos
(
t
)
, with
y
(
0
)
=
0
,
y
′
(
0
)
=
1
y(0)=0, y'(0)=1
y
(
0
)
=
0
,
y
′
(
0
)
=
1
. Which of the following is the solution
y
(
t
)
y(t)
y
(
t
)
?
A
y
(
t
)
=
sin
(
t
)
+
1
2
t
sin
(
t
)
y(t) = \sin(t) + \frac{1}{2}t\sin(t)
y
(
t
)
=
sin
(
t
)
+
2
1
t
sin
(
t
)
B
y
(
t
)
=
cos
(
t
)
+
t
sin
(
t
)
y(t) = \cos(t) + t\sin(t)
y
(
t
)
=
cos
(
t
)
+
t
sin
(
t
)
C
y
(
t
)
=
sin
(
t
)
+
1
2
t
cos
(
t
)
y(t) = \sin(t) + \frac{1}{2}t\cos(t)
y
(
t
)
=
sin
(
t
)
+
2
1
t
cos
(
t
)
D
y
(
t
)
=
sin
(
t
)
y(t) = \sin(t)
y
(
t
)
=
sin
(
t
)
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