The slope field for an unknown differential equation exhibits the following features:…

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

Problem

The slope field for an unknown differential equation exhibits the following features: • All segments on the

x

-axis are horizontal. • The slope at

(2,1)

2

. • The slope at

(-1,1)

-1

. Which of the following differential equations is most consistent with these observations? (a)

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

(b)

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

(c)

\dfrac{dy}{dx}=xy

(d)

\dfrac{dy}{dx}=x^{2}y