Science:Math Exam Resources/Courses/MATH103/April 2012/Question 02 (f)
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Question 02 (f) 

Short answer question. Simplify your answer to the best possible. Show in detail how you arrive at your answer (work will be considered for this problem). Show that is a solution to the differential equation 
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 

You do not need to solve the differential equation to answer this question. You are just asked to show that the given function is a solution. 
Hint 2 

Try finding using the quotient rule and plugging and into the expression . If you can show that this expression is equal to , you will have shown that is a solution to the differential equation. 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. In order to see if satisfies the differential equation, we need to find , substitute and into the left side of the differential equation, and see if the resulting expression is equal to 1. Thus, first, we calculate . Then we plug and into the left hand side of the differential equation. Because this equals the right hand side of the original differential equation, the solution is correct. 