Question

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

A) x=0, only

B) y=0, only

C) y=-5, only

D) y=5, only

E) x=0 or y=-5

Answer 1

E) x=0 or y=-5

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