When will the slope field for the differential equation $\frac{d y}{d x} = \frac{y x^{2} + x y^{2}}{3 x + y}$ $dy/dx=(yx^2+xy^2)/(3x+y)$ have horizontal segments?

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When will the slope field for the differential equation $\frac{d y}{d x} = \frac{y x^{2} + x y^{2}}{3 x + y}$ $dy/dx=(yx^2+xy^2)/(3x+y)$ have horizontal segments?

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Answer 1 · 2018-05-13T20:57:41

Horizontal segments occur then the slope ( $\frac{d y}{d x}$ $dy/dx$ ) equals $0$ $0$ .

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

$x y (x + y) = 0$ $xy(x + y) = 0$

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

Here is the final slope field.
enter image source here

Hopefully this helps!

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When will the slope field for the differential equation $\frac{d y}{d x} = \frac{y x^{2} + x y^{2}}{3 x + y}$ $dy/dx=(yx^2+xy^2)/(3x+y)$ have horizontal segments?

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When will the slope field for the differential equation dydx=yx2+xy23x+ydy/dx=(yx^2+xy^2)/(3x+y) have horizontal segments?

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When will the slope field for the differential equation $\frac{d y}{d x} = \frac{y x^{2} + x y^{2}}{3 x + y}$ $dy/dx=(yx^2+xy^2)/(3x+y)$ have horizontal segments?