A slope field is shown in which all segments along the horizontal line are horizontal

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A slope field is shown in which all segments along the horizontal line

y=2

are horizontal. For points with

y<2

, the segments tilt downward and become steeper as

y

decreases, while for points with

y>2

they tilt upward and become steeper as

y

increases. The slopes do not appear to vary with

x

. Which differential equation is most consistent with the field? (a)

\dfrac{dy}{dx}=2-y

(b)

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

(c)

\dfrac{dy}{dx}=y-2

(d)

\dfrac{dy}{dx}=x-2