Science:Math Exam Resources/Courses/MATH102/December 2017/Question 06

MATH102 December 2017

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Question 06
Match the slope field below to the corresponding differential equation. A. ${\textstyle \displaystyle y'=y(y-1)(y-2)}$ Template:0 B. ${\textstyle \displaystyle y'=-y(y-1)(y-2)}$ C. ${\textstyle \displaystyle y'=-y(y-1)^{2}(y-2)}$ Template:0 D. ${\textstyle \displaystyle y'=(y-1)^{2}(y-2)^{2}}$ E. ${\textstyle \displaystyle y'=y^{2}(y-2)}$ Template:0 F. ${\textstyle \displaystyle y'=y(y-1)^{2}}$

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
In the differential equation, the left hand side is the slope and the right hand side is determined by the height.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. We notice that the slope field is always horizontal at ${\textstyle y=0,1,2}$. This means that we must have the cubic polynomial ${\textstyle y(y-1)(y-2)}$ on the right hand side. This leaves us the choices A, B and C. Observe also that across ${\textstyle y=1}$, the slope is always non-negative. Therefore, the right hand side must carry ${\textstyle (y-1)^{2}}$. It is now easy to check that the slope field is consistent with the differential equation given by C. Answer: ${\textstyle {\color {blue}C}}$.