When will the slope field for the differential equation $\frac{2 x}{4 y - x y}$ $(2x)/(4y-xy)$ have vertical segments?

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Answer 1 · 2018-06-29T06:25:47

I’m assuming the differential equation is $\frac{d y}{d x} = \frac{2 x}{4 y - x y}$ $dy/dx = (2x)/(4y -xy)$

We know that slope will be vertical when $\frac{d y}{d x}$ $dy/dx$ is undefined.

This will occur when $4 y - x y = 0 \to y (4 - x) = 0 \to y = 0 or x = 4$ $4y-xy = 0-> y(4 -x)=0 ->y=0 or x = 4$

Hopefully this helps!

When will the slope field for the differential equation 2x4y−xy(2x)/(4y-xy) have vertical segments?