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

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 

Science:Math Exam Resources/Courses/MATH215/April 2014/Question 01 (a)/Hint 1 
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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There are several ways to solve this question. We will use the integrating factor method: Multiplying the equation by , we find that
Now integrate this equation from 0 to t:
(here we have used the dummy variable s to avoid confusion with the variable t). The lefthand side evaluates to
while the righthand side evaluates (via an integration by parts) to
Equating the two, we see that Therefore, . 