Science:Math Exam Resources/Courses/MATH101/April 2009/Question 06 (b)
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Question 06 (b) 

Solve the differential equation: (Give the general solution) 
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 using an integrating factor. 
Hint 2 

Try using an integrating factor of (so multiply both sides of the equation by this factor). This in the exponent of e comes from the coefficient of the y term in the differential equation. 
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. Following the hint, we multiply both sides by the integrating factor to get The point of the integrating factor is that we can now express the left hand side as simple derivative: Plugging this into the initial equation above we find and by integrating both sides we obtain Solving for y yields completing the question. 