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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

Respuesta :

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

[tex]xy + 5x = 0[/tex]

[tex]x(y + 5) = 0[/tex]

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

So the correct answer is:

E) x=0 or y=-5

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