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

May 13, 2018

Horizontal segments occur then the slope ($\frac{\mathrm{dy}}{\mathrm{dx}}$) equals $0$.

$y {x}^{2} + x {y}^{2} = 0$

$x y \left(x + y\right) = 0$

Thus whenever $x = - y$ and whenever $x \mathmr{and} y = 0$, the given differential equation will have a slope field with horizontal segments.

Here is the final slope field.

Hopefully this helps!