Consider the three differential equations below

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

Problem

Consider the three differential equations below. I. dydx=x−y\dfrac{dy}{dx}=x-y II. dydx=y−x\dfrac{dy}{dx}=y-x III. dydx=x+y\dfrac{dy}{dx}=x+y A certain slope field has horizontal line segments at every point on the line y=xy=x, and on the line y=−xy=-x each segment has slope 2x2x. Indicate which equation (I, II, or III) produces this slope field.

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