The differential equation arises in a physics problem

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

The differential equation

\dfrac{dy}{dx}=\dfrac{4}{1+16x^{2}}

arises in a physics problem. Which of the following functions

y

is an antiderivative of the right–hand side? (a)

y=\dfrac{1}{4}\arctan(4x)+C

(b)

y=\arctan\!\left(\dfrac{x}{4}\right)+C

(c)

y=\arctan(4x)+C

(d)

y=\arcsin(4x)+C