Question

The slope field for the differential equation dy/dx=(3y)/(xy+5x) will have vertical segments when

Answer 1

Answer:

E) x=0 or y=-5

Step-by-step explanation:

The slope field will have vertical segments when dy/dx is undefined, that is, dy/dx is a division by 0.

We have that

dy/dx=(3y)/(xy+5x)

So the slope field will have vertical segments when

$xy + 5x = 0$

$x(y + 5) = 0$

This is when x = 0 or y = -5.

So the correct answer is:

E) x=0 or y=-5