Science:Math Exam Resources/Courses/MATH105/April 2018/Question 02 (c)
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Question 02 (c) 

Solve the following initial value problem: 
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 

Observe that the given equation is a separable differential equation. 
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. Since the given equation is separable, we can rewrite is as Taking integral on the both side of the equation, we have Note that using substitution for any fixed number , we have Applying this for and , we obtain and
where and are arbitrary constants.
Therefore, we get
which can be simplified as follows
We plug to find the constant , Finally, taking a logarithm to the simplified equation, we can find the solution
