A family of differential equations is given by where is a positive constant

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

Problem

A family of differential equations is given by

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

where

k

is a positive constant. A particular slope field generated from this family shows that all line elements on the line

y=x

are horizontal, with slopes positive above the line and negative below it. Which value of

k

produces this field? (a)

k=2

(b)

k=1

(c)

k=0.5

(d)

k=3