Apentix/AP Calculus AB/Unit 7: Differential Equations/Question
AP Calculus ABhardmcq1 pt

Which of the following differential equations has a slope field in which the segment at (2,2)(2,2) has slope 22 and the segment at (2,1)(2,1) has slope 44?

A.dydx=x+y−2\dfrac{dy}{dx} = x + y - 2
B.dydx=x2y\dfrac{dy}{dx} = \dfrac{x^2}{y}
C.dydx=xy\dfrac{dy}{dx} = xy
D.dydx=y2x\dfrac{dy}{dx} = \dfrac{y^2}{x}

Explanation

Core Concept

At (2,2)(2,2) the slope is 42=2\dfrac{4}{2} = 2, and at (2,1)(2,1) it is 41=4\dfrac{4}{1} = 4, so both given slopes match.

Correct Answer

Bdydx=x2y\dfrac{dy}{dx} = \dfrac{x^2}{y}

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