A certain slope field is symmetric with respect to the line ; that is

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

Problem

A certain slope field is symmetric with respect to the line

y=x

; that is, the slope at

(a,b)

equals the slope at

(b,a)

for all real numbers

a

and

b

. Which of the following differential equations cannot produce such a symmetric slope field? (I)

\dfrac{dy}{dx}=x-y

(II)

\dfrac{dy}{dx}=xy

(III)

\dfrac{dy}{dx}=x+y

State the Roman numeral of the equation that is inconsistent with the stated symmetry.