Question

When will the slope field for the differential equation `dy/dx=(yx^2+xy^2)/(3x+y)` have horizontal segments?

Answer 1

See below.

Explanation:

`dy/dx=(yx^2+xy^2)/(3x+y)`

now `dy/dx=0 rArr xy(x+y)=0 rArr {(x=0),(y=0),(x+y=0):}`

Attached a plot showing the equilibrium locus in dashed red.