Mathematics

Problem

A slope field satisfies the following observations: • Segments are horizontal along the line

x+y=1

. • Along the parallel line

x+y=4

, segments have slope

9

. Assume the differential equation has the form

\displaystyle \frac{dy}{dx}=k\,(x+y-1)

, where

k

is a nonzero constant. Determine the value of

k

and write the complete differential equation.