In a slope field it is observed that

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

Problem

In a slope field it is observed that, for every vertical line

x=k

, the slope at any point on that line equals

k^{2}

. Which differential equation below is consistent with this observation? (I)

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

(II)

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

(III)

\dfrac{dy}{dx}=xy

Write the Roman numeral of the correct choice.