A slope field is observed in which • All slope segments along the vertical axis x = 0…

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

Problem

A slope field is observed in which • All slope segments along the vertical axis x = 0 are horizontal (slope = 0). • Moving to the right, the slope segments become increasingly positive, while moving to the left they become increasingly negative. • At a fixed x–value, the slope appears the same for all y–values. Which differential equation best matches the described slope field? (a) dydx=xy\dfrac{dy}{dx}=xy (b) dydx=x2\dfrac{dy}{dx}=x^{2} (c) dydx=x\dfrac{dy}{dx}=x (d) dydx=y\dfrac{dy}{dx}=y

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