Consider the differential equation

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

\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)

(b)

y=\tanh(\cos x + C)

(c)

y=\tanh(\sin x + C)

(d)

y=\cosh(\sin x + C)