Question

Which are true about the differential equation dy/dx = 2x(4-y)

I.will have a slope field with negative slopes in quadrant I
II.will have a slope field with positive slopes in all quadrants
III.will produce a slope field with columns of parallel tangents

Answer 1

I is true sometimes -- e.g., at (2,5)
II is true sometimes -- e.g., at (1,1),(-1,5),(-1,1),(1,-5)
III is clearly false. In a column at x=h, the tangents will get more negative as y increases.

I think the question is poorly worded.