Science:Math Exam Resources/Courses/MATH215/December 2011/Question 01 (b)
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Question 01 (b) 

Solve the following nonlinear ODE: 
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 

The substitution will simplify matters. 
Hint 2 

After the substitution you will recover a differential equation that you are familiar with. 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. As the exam hint suggests, we make the substitution so that
Under this substitution, becomes
where we multiplied the equation by This is now the same ODE as in part (a), so the solution is that . Hence we have
