MATH101 April 2010
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Find the solution of the differential equation
that satisfies . Here, is a constant that will appear in your final answer.
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!
Can you separate the variables and ?
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Beginning with the equation
we separate the variables and to obtain
If we then integrate both sides of this equation (ignoring the constant of integration in the first case) we find that
and using integration by parts we find that
and so if we set the two of these equal to each other we find that
If we solve for we find
Since it follows that and so
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