Science:Math Exam Resources/Courses/MATH101/April 2006/Question 04 (a)
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Question 04 (a)
Full-Solution Problems. Justify your answers and show all your work. Simplification of answers is not required.
Solve the initial value problem
subject to the initial condition . Express your answer in the form and simplify your answer completely.
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!
Try separating variables.
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First, by separating variables, we have
Then, integrating both sides yields
Under the initial condition , we have
and so we have
and simplifying, we have
completing the question.