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Mathematics
Mathematics
Problem
Which of the following expressions gives
y
(
x
)
y(x)
y
(
x
)
, the particular solution to the differential equation
d
y
d
x
=
cos
x
\dfrac{dy}{dx}=\cos x
d
x
d
y
=
cos
x
that satisfies
y
(
0
)
=
2
y(0)=2
y
(
0
)
=
2
? a)
y
(
x
)
=
2
−
∫
0
x
cos
t
d
t
y(x)=2-\displaystyle\int_{0}^{x}\cos t\,dt
y
(
x
)
=
2
−
∫
0
x
cos
t
d
t
b)
y
(
x
)
=
2
+
∫
0
x
cos
t
d
t
y(x)=2+\displaystyle\int_{0}^{x}\cos t\,dt
y
(
x
)
=
2
+
∫
0
x
cos
t
d
t
c)
y
(
x
)
=
∫
0
x
cos
t
d
t
y(x)=\displaystyle\int_{0}^{x}\cos t\,dt
y
(
x
)
=
∫
0
x
cos
t
d
t
d)
y
(
x
)
=
2
cos
x
y(x)=2\cos x
y
(
x
)
=
2
cos
x
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