Science:Math Exam Resources/Courses/MATH215/April 2014/Question 01 (b)
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Question 01 (b)
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?
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Try factoring the right-hand side.
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Note that we can factor the right-hand 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 ,
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.