Science:Math Exam Resources/Courses/MATH101/April 2007/Question 04 (a)
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Question 04 (a) 

FullSolution Problem. Justify your answers and show all your work. Simplification of answers is not required. Find the general solution of the differential equation . 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Try bringing the term over first. Then integrating both sides once is easy. 
Hint 2 

Next, try an integrating factor. 
Hint 3 

Multiply both sides by . Then integrate. 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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. Bringing the term over we have
Integrating both sides yields
Now, bring the y term to the left and dividing by , we have
Now, multiplying both sides by yields
The left hand side is now a product rule derivative, namely
Integrating both sides yields
Dividing both sides by gives
completing the question. 