The slope field of an unknown differential equation has these properties:

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

The slope field of an unknown differential equation has these properties: (i) all segments are horizontal along the line

y=1

; (ii) all segments have slope

4

along the line

y=3

; (iii) the slope at the point

(2,2)

equals

2

. Indicate which equation is consistent with the field and give its identifying letter: A.

\displaystyle \dfrac{dy}{dx}=(y-1)(y-3)

\displaystyle \dfrac{dy}{dx}=y-1

\displaystyle \dfrac{dy}{dx}=2(y-1)