Question

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

Answer 1

Horizontal segments occur then the slope (`dy/dx`) equals `0`.

`yx^2 + xy^2 = 0`

`xy(x + y) = 0`

Thus whenever `x = -y` and whenever `x or y = 0`, the given differential equation will have a slope field with horizontal segments.

Here is the final slope field.

Hopefully this helps!