Mathematics

Problem

For differentiable functions

x(t)

and

y(t)

, a verbal description states, “the rate of change of

x

is proportional to

y

.” Which of the following equations best models this description for some constant of proportionality

k

? a)

\dfrac{dx}{dt}=k\,x\,y

\dfrac{dy}{dt}=k\,y

\dfrac{dx}{dt}=k\,y

\dfrac{d^{2}x}{dt^{2}}=k\,y