A slope field displays the following features: • All segments on either axis ( or )…

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

Problem

A slope field displays the following features: • All segments on either axis (x=0x=0 or y=0y=0) are horizontal. • In Quadrants I and III the segments tilt upward; in Quadrants II and IV they tilt downward. • The pattern is symmetric with respect to a 180∘180^{\circ} rotation about the origin. Which differential equation best models this field? (a) dydx=x+y\dfrac{dy}{dx}=x+y (b) dydx=xy\dfrac{dy}{dx}=xy (c) dydx=x2y2\dfrac{dy}{dx}=x^{2}y^{2} (d) dydx=yx\dfrac{dy}{dx}=\dfrac{y}{x}

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