calculus question

Question

Which of the following differential equations is consistent with the following slope field?

 (5 points)

Answer 1

The thing to look at is the slope of the derivative in each quadrant.

In quadrant II (x < 0, y > 0) the slope is positive, which eliminates

dy/dx = x/y² and

dy/dx = x/y

Because for those the right hand side is negative in quadrant II.

In quadrant IV (x < 0, y < 0) the slope is negative.

That eliminates

dy/dx = x²/y²

which is always positive.

The remaining

dy/dx = x²/y

is consistent with the slope field in all quadrants.