Differential Equation HELP ASAP PLSSS!!

Question

 

The differential equation  (5 points)

1. produces a slope field with vertical tangents at y = 3
2. produces a slope field with vertical tangents at x = -1
3. produces a slope field with rows of parallel segments

Answer Choices:

	I only
	II only
	III only
	I and III

Answer 1

You can see it by considering what the equation dy/dx means. Its the slope of the solution at each point. You do not have to draw an entire direction field, you can just figure out what a vertical slope, vertical tangents and parallel segments means in terms of the given differential equation.

Vertical tangents means the slope is approaching infinity, or going straight up or down. If you plug in y=3 into the equation, you would be dividing by zero, which causes infinite slopes. Technically, its true to say that as y approaches 3, the slope goes vertical.

rows of parallel segments means that the field has dy/dx = 0 for many values.

Check y=3 : dy/dx goes to infinity which is a vertical tangent.

x = -1: dy/dx = -1 +1 / y-3 = 0 This is a horizontal line for every value of y. So, parallel segments. but no vertical ones.

So the answer is D, 1&3 only.