Mathematics

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

k=1

k=0.5

k=3