Mathematics

Problem

A slope field has the following property: at every point with

x=0

the line segments have slope

-1

; at every point with

x=1

the segments are horizontal; and at every point with

x=2

the segments have slope

1

. Which differential equation is most consistent with these observations? a)

\dfrac{dy}{dx}=1-x

\dfrac{dy}{dx}=x(x-1)

\dfrac{dy}{dx}=x-1

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