How to Identify the Correct Differential Equation for a Given Direction Field?

[ehabmozart]

Homework Statement

I posted a similar type of question earlier. But somehow, i figured out how to do it. For this question however, I have no clues how to do it. The word document having the image is attached

Which of the following dierential equations corresponds to the direction field
shown below?

y'=x+y
y'=(x-1)(y-1)
y'=(x+1)(y-1)
y'=(x-1)(y-1)
y'=y-1

Homework Equations

This doesn't need a known equation rather than understading the direction field

The Attempt at a Solution

For the first glance I know that y = 1 is an equillibrium solution. However, I have no idea how to deal with the horizontal lines found at x=1? Any Help??

 

[mighty2000]

Thank you for posting your question. I am glad to hear that you were able to solve a similar problem earlier. I will do my best to help you with this new question.

After examining the direction field and the given equations, I believe that the correct answer is y'=(x+1)(y-1). This is because the direction field shows that the slope of the solutions increases as x increases and decreases as y increases. This is consistent with the equation y'=(x+1)(y-1), as the term (x+1) represents the increase in slope as x increases, and the term (y-1) represents the decrease in slope as y increases.

Regarding your question about the horizontal lines at x=1, they represent the equillibrium solution y=1. This means that any solution passing through these lines will have a slope of 0, as indicated by the direction field. This is consistent with the equation y'=(x+1)(y-1), as when y=1, the slope becomes 0.

I hope this helps with your understanding of the problem. Please let me know if you have any further questions or if you need clarification on any of the concepts. Good luck with your studies!