Science:Math Exam Resources/Courses/MATH215/April 2014/Question 01 (b)
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Question 01 (b) 

Solve for , subject to . 
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 

Try factoring the righthand side. 
Checking a solution serves two purposes: helping you if, after having used the hint, 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. Note that we can factor the righthand side: . Therefore
and hence the problem is really just a disguised exercise in separation of variables. Continuing, we find
( a constant of integration), or solving for ,
(where ). The constant is determined from the initial condition ; this gives . Upon simplification, we therefore conclude that
To check our answer, we can differentiate it (exercise) to make sure it does indeed satisfy the given differential equation. 