Science:Math Exam Resources/Courses/MATH103/April 2011/Question 06 (a)
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Question 06 (a) 

Consider the differential equation Find the steady state solution(s). 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

A solution is called "steadystate" if it is constant (i.e. if there is some such that for all ). 
Hint 2 

What is the derivative of a steady state solution? 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The steady state solutions are solutions to the differential equation that are constant. That is, . For this to be possible, the derivative of has to be zero. Therefore, to be consistent with the differential equation, we have that . For this equation to be true, we require that or . Since does not fit the definition of a steady state solution, we are left with the steady solutions . 