Mathematics

Problem

Consider the differential equation

\dfrac{dy}{dx}=(1-y^{2})\cos x

. Which of the following families of functions satisfies the equation for all real numbers

x

on any interval where the function is defined? (Here

C

is an arbitrary constant.) a)

y=\tan(\sin x + C)

y=\tanh(\cos x + C)

y=\tanh(\sin x + C)

y=\cosh(\sin x + C)