Science:Math Exam Resources/Courses/MATH101/April 2010/Question 07
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Question 07 

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! 
Hint 

Can you separate the variables and ? 
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. 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 