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Mathematics
Problem
The differential equation
d
y
d
x
=
4
1
+
16
x
2
\dfrac{dy}{dx}=\dfrac{4}{1+16x^{2}}
d
x
d
y
=
1
+
16
x
2
4
arises in a physics problem. Which of the following functions
y
y
y
is an antiderivative of the right–hand side? a)
y
=
1
4
arctan
(
4
x
)
+
C
y=\dfrac{1}{4}\arctan(4x)+C
y
=
4
1
arctan
(
4
x
)
+
C
b)
y
=
arctan
(
x
4
)
+
C
y=\arctan\!\left(\dfrac{x}{4}\right)+C
y
=
arctan
(
4
x
)
+
C
c)
y
=
arctan
(
4
x
)
+
C
y=\arctan(4x)+C
y
=
arctan
(
4
x
)
+
C
d)
y
=
arcsin
(
4
x
)
+
C
y=\arcsin(4x)+C
y
=
arcsin
(
4
x
)
+
C
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