Mathematics

Problem

In the slope field for the differential equation

\dfrac{dy}{dx}=f(x,y)

, every segment lying on the horizontal line

y=3

is horizontal. Which of the following must be true? a)

f(3,y)=0

for all real

y

. b)

f(x,3)=3

for all real

x

. c)

f(x,3)=0

for all real

x

. d)

f(3,3)=0

, but

f(x,3)\neq0

for some

x\neq3